結論與展望

本研究採用共旋轉有限元素法探討不同設定角、傾斜角之等速旋轉的 三維傾斜尤拉梁的穩態變形及以該穩態變形為平衡點的微小振動之自然振 動頻率。本文中考慮梁的軸向、兩個側向位移及扭轉之三維運動，本研究 採用 d'Alembert 原理、虛功原理、幾何非線性梁理論的一致線性化，在梁 元素當前之元素座標上推導節點慣性力和節點變形力，再將元素的節點力 轉到總體座標後組合成系統的非線性運動方程式。本研究將旋轉梁的運動 方程式中函時間函數的項去掉，求得系統穩態平衡方程式，再用基於牛頓 法的增量迭代法求出所有位移以及扭轉的穩態解，將運動方程式在穩態平 衡位置用泰勒級數展開，取到一次項，求得旋轉傾斜梁的振動方程式，再 假設自然振動頻率存在，可求得一組代數齊次方程式，該組齊次方程式係 數形成之矩陣的行列式為零時，即可求得旋轉梁以穩態解為平衡點的自然 振動的頻率及其對應的振態。

由本研究的數值例題可以得到以下的結論：

1.

當設定角不為

0

^o或

90

^o，若傾斜角不為

0

^o時，三維旋轉梁結構的穩態解 包含著軸向、扭轉以及兩個側方向位移，此時以穩態解為平衡點的振動是 軸向、扭轉及兩個側向耦合的振動，且耦合的程度隨著傾斜角

α

^{、無因次轉} 速

k

和梁的細長比的增加而增加。

2. 當傾斜角

α ≠ 0

^{o，設定角}

β = ⁰

^o或

⁹⁰

^o時，旋轉梁的穩態解僅有軸向及一 個側方向的位移。

3.

傾斜角

α = 0

^{o且設定角}

β ≠ ⁰

^o或

⁹⁰

^o時，穩態解僅有軸向、扭轉的變形，且 這個扭轉變形會與軸向變形產耦合作用。當

I

_y和

I

_z的值差距越大，穩態解 的扭轉變形也越大。因科式力的關係，其側向與扭轉變形的振動是耦合的。

4. 具有任意設定角和傾斜角的旋轉梁結構之最大無因次轉速可以由穩態解時 之最大膜應變分別和兩個側向最大撓曲應變知何來決定，當傾斜角為零度 時，因無側向變形，故不會產生撓曲應變，所以當無因次轉速半徑

r = 0

時之 最大無因次轉速

k

可設為

0 . 1

；在傾斜角不為零度時，因須考慮最大撓曲應變，

最大無因次轉速

k

約為

0 . 01

。

5.

當設定角為

0

^o時，因無因次振動頻率

K

隨著轉速增加的速度不同，使不同 振態的頻率隨著轉速增加而接近，產生了頻率曲線交錯或是交叉的現象，而 細長比較小的側向振動會有很大的扭轉振動分量，造成徵值曲線轉向

(Eigenvalue curve veering)

及振態交換的現象。因頻率的增加率會隨著細

長比與轉速增加而變大，故細長比不同之兩軸側向振動所對應的頻率會 有彼此交叉的情況。

5.2

未來展望

1.

本研究僅探討設定角、傾斜角對旋轉梁的所造成影響，但旋轉梁另外還有

預扭角

(Pretwised angle)

和預錐角

(Precone angle)

，這些都會影響旋轉梁的

穩態解及自然振動頻率，在將來亦非常值得探討。

2.

因旋轉梁的自由端常加掛配重，藉此來改善旋轉梁結構之機能性。例如增加 渦輪風扇的氣流，增加撓性旋轉葉片的撓度，或是改善旋轉梁結構之自然振 動頻率等，故將來擬推導旋轉梁的運動方程式時應將配重考慮進去。

參考文獻

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^th

Edition, John Wiley & Sons Inc, New Jersey.

表一 不同橢圓斷面的收斂分析 (

k = 0 . 1

、

α = 0

^o、

β = ⁴⁵

^o、

r = ¹

)

=5 b

a ，L_T a=50 a b=10，L_T a=50

元素數目 10 20 40 50 20 30 40 50

ε0 1.42324E-2 1.44842E-2 1.46072E-2 1.46315E-2 1.44835E-2 1.45656E-2 1.46064E-2 1.46309E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 V_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 W_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 3.33458E-2 3.36640E-2 3.37781E-2 3.37922E-2 9.44427E-2 9.46527E-2 9.47467E-2 9.48000E-2 )

1 . 0

1(

Θ′ 4.93207E-2 5.81485E-2 5.87462E-2 5.87461E-2 1.49635E-1 1.51590E-1 1.51659E-1 1.51673E-1

K1 1.26477E-1 1.26137E-1 1.26058E-1 1.26050E-1 1.25628E-1 1.25517E-1 1.25478E-1 1.25416E-1 K2 1.62721E-1 1.62511E-1 1.62464E-1 1.62459E-1 1.62211E-1 1.62163E-1 1.62148E-1 1.62090E-1 K 3 3.73547E-1 3.70702E-1 3.69838E-1 3.69733E-1 2.57620E-1 2.57326E-1 2.57209E-1 2.57154E-1 K4 4.14920E-1 4.12991E-1 4.12307E-1 4.12222E-1 3.67405E-1 3.66632E-1 3.66333E-1 3.66160E-1 K 5 4.39860E-1 4.38333E-1 4.37948E-1 4.37902E-1 4.37458E-1 4.37167E-1 4.37065E-1 4.36487E-1 K 6 6.20781E-1 6.13537E-1 6.11323E-1 6.11052E-1 5.95181E-1 5.92856E-1 5.91937E-1 5.91431E-1 K 7 8.87731E-1 8.83230E-1 8.81246E-1 8.80981E-1 7.21760E-1 7.20875E-1 7.20521E-1 7.20354E-1 K 8 8.98613E-1 8.90328E-1 8.88710E-1 8.88545E-1 8.35416E-1 8.31632E-1 8.30149E-1 8.29282E-1

表二 不同橢圓斷面的收斂分析 (

k = 0 . 03

、

α = 5

^o、

β = ⁴⁵

^o、

r = ¹

)

=5 b

a ，L_T a=50 a b=10，L_T a=50

元素數目 10 20 40 50 20 30 40 50

ε0 1.29432E-3 1.31545E-3 1.32489E-3 1.32665E-3 1.31574E-3 1.32160E-3 1.32425E-3 1.32580E-3 εb -3.30661E-3 -3.68072E-3 -3.81227E-3 -3.82957E-3 -3.38148E-3 -3.62400E-3 -3.72389E-3 -3.77186E-3 εc 3.54103E-3 3.57432E-3 3.58288E-3 3.58383E-3 3.61204E-3 3.61795E-3 3.61984E-3 3.62060E-3 V_tip -4.93470E-2 -4.93995E-2 -4.94086E-2 -4.94094E-2 -5.15768E-2 -5.15975E-2 -5.16021E-2 -5.16032E-2 W_tip 3.34203E-2 3.34543E-2 3.34616E-2 3.34623E-2 3.39254E-2 3.39358E-2 3.39379E-2 3.39380E-2

) 1

1(

Θ -2.10380E-3 -2.46365E-3 -2.65599E-3 -2.68060E-3 2.84228E-3 2.63256E-3 2.37216E-3 2.30312E-3 )

1 . 0

1(

Θ′ 8.34102E-3 -6.07496E-3 -6.87900E-3 -6.87171E-3 2.12194E-2 1.78888E-2 1.79272E-2 1.79739E-2

K1 4.22616E-2 4.22362E-2 4.22282E-2 4.22273E-2 4.11694E-2 4.11765E-2 4.11811E-2 4.11841E-2 K2 5.82322E-2 5.81987E-2 5.81908E-2 5.81899E-2 5.80876E-2 5.80957E-2 5.80992E-2 5.81010E-2 K 3 1.21500E-1 1.20999E-1 1.20863E-1 1.20846E-1 1.12776E-1 1.12624E-1 1.12568E-1 1.12542E-1 K4 2.26669E-1 2.25832E-1 2.25611E-1 2.25584E-1 1.89034E-1 1.88571E-1 1.88393E-1 1.88306E-1 K 5 2.48002E-1 2.47901E-1 2.47883E-1 2.47881E-1 2.03335E-1 2.03242E-1 2.03214E-1 2.03205E-1 K 6 3.65120E-1 3.63839E-1 3.63505E-1 3.63461E-1 2.47699E-1 2.47714E-1 2.47728E-1 2.47738E-1 K 7 3.83321E-1 3.81477E-1 3.80873E-1 3.80803E-1 2.88773E-1 2.88355E-1 2.88207E-1 2.88136E-1 K 8 5.38561E-1 5.36707E-1 5.36383E-1 5.36346E-1 3.98665E-1 3.98063E-1 3.97844E-1 3.97739E-1

表三 不同橢圓斷面的收斂分析 (

k = 0 . 01

、

α = 30

^o、

β = ⁴⁵

^o、

r = ¹

)

=5 b

a ，L_T a=50 a b=10，L_T a=50

元素數目 10 20 40 50 20 30 40 50

ε0 1.14396E-4 1.10341E-4 1.09169E-4 1.09502E-4 -8.89930E-5 -1.00579E-4 -8.96666E-5 -7.20208E-5 εb -6.36862E-3 -6.37139E-3 -6.31583E-3 -6.29968E-3 -5.73327E-3 -5.26737E-3 -4.98644E-3 -4.80546E-3 εc 3.60710E-3 3.60855E-3 3.60532E-3 3.60411E-3 3.36886E-3 3.35036E-3 3.34148E-3 3.33641E-3 V_tip -2.23005E-1 -2.23567E-1 -2.23751E-1 -2.23772E-1 -2.98552E-1 -2.99439E-1 -2.99756E-1 -2.99895E-1 W_tip 5.09794E-2 5.13255E-2 5.14510E-2 5.14649E-2 8.83667E-2 8.99064E-2 9.05163E-2 9.08061E-2

) 1

1(

Θ -6.42035E-2 -6.72246E-2 -6.82736E-2 -6.83990E-2 -2.87797E-1 -2.95026E-1 -2.97762E-1 -2.98966E-1 )

1 . 0

1(

Θ′ -1.68979E-1 -2.44817E-1 -2.49441E-1 -2.49484E-1 -1.23601E+0 -1.26494E+0 -1.26869E+0 -1.27047E+0

K1 1.51128E-2 1.53558E-2 1.53645E-2 1.53643E-2 1.21773E-2 1.22106E-2 1.22173E-2 1.22197E-2 K2 3.57412E-2 3.57667E-2 3.57501E-2 3.57478E-2 2.31811E-2 2.31290E-2 2.30488E-2 2.30000E-2 K 3 5.57016E-2 5.67042E-2 5.67524E-2 5.67525E-2 4.12232E-2 4.12832E-2 4.12795E-2 4.12725E-2 K4 1.34163E-1 1.36271E-1 1.36388E-1 1.36389E-1 8.59769E-2 8.64412E-2 8.65383E-2 8.65717E-2 K 5 2.20596E-1 2.20251E-1 2.20127E-1 2.20111E-1 1.41663E-1 1.42655E-1 1.42829E-1 1.42881E-1 K 6 2.51863E-1 2.54757E-1 2.54979E-1 2.54984E-1 1.92582E-1 1.91327E-1 1.90592E-1 1.90181E-1 K 7 3.92998E-1 3.90513E-1 3.89770E-1 3.89679E-1 2.20557E-1 2.20588E-1 2.20597E-1 2.20600E-1 K 8 4.08788E-1 4.11482E-1 4.11735E-1 4.11736E-1 2.38958E-1 2.40129E-1 2.40444E-1 2.40566E-1

表四 不同橢圓斷面的收斂分析 (

k = 0 . 01

、

α = 45

^o、

β = ⁴⁵

^o、

r = ¹

)

=5 b

a ，L_T a=50 a b=10，L_T a=50

元素數目 10 20 40 50 20 30 40 50

ε0 5.94371E-5 4.18359E-5 3.97925E-5 4.24494E-5 -6.81821E-4 -6.94612E-4 -6.47886E-4 -5.84347E-4 εb -9.59982E-3 -9.37689E-3 -9.13876E-3 -9.08062E-3 -8.59202E-3 -7.62946E-3 -7.06680E-3 -6.70674E-3 εc 4.95201E-3 4.93693E-3 4.92146E-3 4.91702E-3 3.64653E-3 3.60388E-3 3.58334E-3 3.57148E-3 V_tip -3.52077E-1 -3.53694E-1 -3.54233E-1 -3.54294E-1 -4.86462E-1 -4.86349E-1 -4.86263E-1 -4.86204E-1 W_tip 8.74405E-2 8.89836E-2 8.95496E-2 8.96162E-2 2.28017E-1 2.30867E-1 2.31988E-1 2.32526E-1

) 1

1(

Θ -1.50962E-1 -1.58394E-1 -1.60951E-1 -1.61260E-1 -6.19329E-1 -6.24650E-1 -6.26237E-1 -6.27223E-1 )

1 . 0

1(

Θ′ -4.20038E-1 -5.89371E-1 -6.00259E-1 -6.00452E-1 -2.70549E+0 -2.72196E+0 -2.71114E+0 -2.70566E+0

K1 1.34791E-2 1.41519E-2 1.41799E-2 1.41805E-2 1.13431E-2 1.15795E-2 1.16384E-2 1.16619E-2 K2 3.16461E-2 3.19796E-2 3.19136E-2 3.19015E-2 1.88459E-2 1.90696E-2 1.90641E-2 1.90486E-2 K 3 5.28884E-2 5.56465E-2 5.58042E-2 5.58113E-2 4.11164E-2 4.13957E-2 4.14257E-2 4.14259E-2 K4 1.26556E-1 1.32888E-1 1.33276E-1 1.33291E-1 8.40425E-2 8.55675E-2 8.58873E-2 8.60007E-2 K 5 2.13723E-1 2.12911E-1 2.12396E-1 2.12318E-1 1.19399E-1 1.22408E-1 1.22724E-1 1.22754E-1 K 6 2.42744E-1 2.51125E-1 2.51875E-1 2.51924E-1 1.70282E-1 1.70114E-1 1.69511E-1 1.69124E-1 K 7 3.94486E-1 4.04159E-1 4.05028E-1 4.05059E-1 2.35608E-1 2.38485E-1 2.39145E-1 2.39371E-1 K 8 4.15722E-1 4.13383E-1 4.12783E-1 4.12710E-1 2.60690E-1 2.59601E-1 2.59044E-1 2.58753E-1

表五 不同橢圓斷面的收斂分析 (

k = 0 . 01

、

α = 60

^o、

β = ⁴⁵

^o、

r = ¹

)

=5 b

a ，L_T a=50 a b=10，L_T a=50

元素數目 10 20 40 50 20 30 40 50

ε0 -4.66626E-5 -8.92356E-5 -8.79676E-5 -7.86585E-5 **** -1.31990E-3 -1.24867E-3 -1.14706E-3 εb -1.30061E-2 -1.24137E-2 -1.19052E-2 -1.17863E-2 **** -1.17529E-2 -1.10693E-2 -1.06278E-2 εc 5.70746E-3 5.65437E-3 5.61565E-3 5.60551E-3 **** 3.35953E-3 3.32613E-3 3.30495E-3 V_tip -4.94695E-1 -4.97178E-1 -4.97970E-1 -4.98059E-1 **** -6.25463E-1 -6.24988E-1 -6.24745E-1 W_tip 1.41818E-1 1.46033E-1 1.47550E-1 1.47734E-1 **** 3.63422E-1 3.64520E-1 3.65056E-1

) 1

1(

Θ -2.70518E-1 -2.82834E-1 -2.87126E-1 -2.87642E-1 **** -7.89124E-1 -7.88171E-1 -7.90388E-1 )

1 . 0

1(

Θ′ -7.92369E-1 -1.07591E+0 -1.09307E+0 -1.09325E+0 **** -3.49052E+0 -3.46473E+0 -3.45147E+0

K1 1.06813E-2 1.28358E-2 1.29179E-2 1.29222E-2 **** 1.15761E-2 1.17199E-2 1.17693E-2 K2 2.49054E-2 2.76103E-2 2.75456E-2 2.75274E-2 **** 1.82926E-2 1.83417E-2 1.83379E-2 K 3 4.83946E-2 5.47966E-2 5.51124E-2 5.51293E-2 **** 4.12044E-2 4.13701E-2 4.14195E-2 K4 1.09865E-1 1.27663E-1 1.28530E-1 1.28570E-1 **** 7.98808E-2 8.09813E-2 8.13623E-2 K 5 1.95386E-1 1.97973E-1 1.96943E-1 1.96771E-1 **** 1.09138E-1 1.10009E-1 1.10113E-1 K 6 2.29543E-1 2.47451E-1 2.49008E-1 2.49128E-1 **** 1.61702E-1 1.61450E-1 1.61173E-1 K 7 3.67799E-1 3.94977E-1 3.97057E-1 3.97159E-1 **** 2.26731E-1 2.28386E-1 2.28984E-1 K 8 4.55637E-1 4.53952E-1 4.53575E-1 4.53529E-1 **** 2.70943E-1 2.70586E-1 2.70264E-1

表六 不同 I 型斷面的收斂分析 (k =0.01、

α = 45

^o、

β = ⁴⁵

^o、

r = ¹

)

30 10×

W ， L_T /d_nom =25 W10×100， L_T /d_nom =25

元素數目 10 20 40 50 20 30 40 50

ε0 2.81096E-5 7.02953E-5 8.78214E-5 9.03004E-5 1.09264E-4 1.10177E-4 1.10526E-4 1.10583E-4 εb -7.36936E-3 -7.21231E-3 -7.15961E-3 -7.15255E-3 -4.21324E-3 -4.21641E-3 -4.21687E-3 -4.21690E-3 εc 1.65922E-3 1.68729E-3 1.69561E-3 1.69665E-3 1.62242E-3 1.62653E-3 1.62766E-3 1.62779E-3 V_tip -1.53768E-1 -1.53404E-1 -1.53307E-1 -1.53295E-1 -4.95208E-2 -4.95209E-2 -4.95209E-2 -4.95208E-2 W_tip 4.19340E-2 4.15379E-2 4.14349E-2 4.14226E-2 1.84691E-2 1.84634E-2 1.84619E-2 1.84617E-2

) 1

1(

Θ -4.10995E-1 -4.10875E-1 -4.10831E-1 -4.10827E-1 -2.17394E-2 -2.16642E-2 -2.16443E-2 -2.16419E-2 )

1 . 0

1(

Θ′ -9.46509E-1 -9.47643E-1 -9.47882E-1 -9.47913E-1 -5.63754E-2 -5.62460E-2 -5.62098E-2 -5.62052E-2

K1 2.22833E-2 2.24595E-2 2.24975E-2 2.25019E-2 3.96679E-2 3.96674E-2 3.96670E-2 3.96670E-2 K2 4.02783E-2 4.04500E-2 4.04911E-2 4.04958E-2 6.55261E-2 6.55669E-2 6.55770E-2 6.55782E-2 K 3 9.31399E-2 9.21334E-2 9.18804E-2 9.18500E-2 1.32938E-1 1.32811E-1 1.32780E-1 1.32776E-1 K4 1.31111E-1 1.31855E-1 1.32037E-1 1.32058E-1 2.36747E-1 2.36731E-1 2.36727E-1 2.36726E-1 K 5 2.66490E-1 2.62834E-1 2.61905E-1 2.61793E-1 4.04107E-1 4.03715E-1 4.03608E-1 4.03595E-1 K 6 3.25313E-1 3.26140E-1 3.26330E-1 3.26352E-1 4.41798E-1 4.42107E-1 4.42202E-1 4.42214E-1 K 7 4.21570E-1 4.24288E-1 4.24943E-1 4.25021E-1 6.56184E-1 6.56022E-1 6.56007E-1 6.56006E-1 K 8 5.13923E-1 5.11642E-1 5.11128E-1 5.11068E-1 8.70369E-1 8.69909E-1 8.69824E-1 8.69814E-1

表七 不同十字斷面的收斂分析 (k =0.01、

α = 45

^o、

β = ⁴⁵

^o、

r = ¹

)

35 . 0 7 14× ×

=

×

×b t

d ，L_T d =10 _{d×b×t =14×7×0.35，}L_T d =20

元素數目 10 20 40 50 20 30 40 50

ε0 -7.12403E-5 -5.39364E-5 1.11874E-5 3.24890E-5 -8.33015E-4 -9.61091E-4 -9.03068E-4 -8.33954E-4 εb -7.96751E-3 -7.82462E-3 -7.73796E-3 -7.72169E-3 -1.37044E-2 -1.27842E-2 -1.21692E-2 -1.20289E-2 εc 2.16671E-3 2.20574E-3 2.22581E-3 2.22935E-3 3.39632E-3 3.62848E-3 3.75236E-3 3.77792E-3 V_tip -7.91020E-2 -7.91978E-2 -7.92189E-2 -7.92198E-2 -2.26582E-1 -2.25725E-1 -2.25492E-1 -2.25467E-1 W_tip 1.83816E-2 1.85565E-2 1.86024E-2 1.86056E-2 1.35541E-1 1.38075E-1 1.39525E-1 1.39776E-1

) 1

1(

Θ -1.80755E-1 -1.84507E-1 -1.85494E-1 -1.85581E-1 -7.94639E-1 -7.98489E-1 -7.99910E-1 -8.00126E-1 )

1 . 0

1(

Θ′ -6.48384E-1 -7.32280E-1 -7.34450E-1 -7.34458E-1 -2.34018E+0 -3.02738E+0 -3.05823E+0 -3.04865E+0

K1 3.12002E-2 3.12283E-2 3.12314E-2 3.12321E-2 1.89056E-2 1.93094E-2 1.93673E-2 1.93711E-2 K2 5.49738E-2 5.47178E-2 5.46219E-2 5.46120E-2 2.72479E-2 2.69202E-2 2.67556E-2 2.67276E-2 K 3 8.64376E-2 8.58571E-2 8.56907E-2 8.56706E-2 8.71187E-2 8.55960E-2 8.51330E-2 8.50706E-2 K4 1.89150E-1 1.89298E-1 1.89341E-1 1.89347E-1 1.01572E-1 1.02809E-1 1.02865E-1 1.02844E-1 K 5 2.04699E-1 2.03750E-1 2.03506E-1 2.03477E-1 1.87791E-1 1.82264E-1 1.80578E-1 1.80351E-1 K 6 3.20803E-1 3.19499E-1 3.19098E-1 3.19054E-1 2.67415E-1 2.70595E-1 2.71009E-1 2.71014E-1 K 7 4.36022E-1 4.33501E-1 4.32621E-1 4.32524E-1 3.18909E-1 3.15832E-1 3.14472E-1 3.14249E-1 K 8 5.03344E-1 5.01865E-1 5.01387E-1 5.01325E-1 4.07388E-1 4.09744E-1 4.10122E-1 4.10144E-1

表八 旋轉傾斜梁在不同橢圓斷面的振動頻率(轉速

k = 0

)

= 5 b

a a b = 10

= 20 a

L

_T

L

_T

a = 50 L

_T

a = 20 L

_T

a = 50

n

y 2.00000E+2 5.00000E+2 4.00000E+2 1.00000E+3

n

z 4.00000E+1 1.00000E+2 4.00000E+1 1.00000E+2

K

1 1.75790E-2(2) 7.03196E-3(2) 8.78991E-3(2) 3.51601E-3(2)

K

2 8.77730E-2(3) 3.51520E-2(3) 5.50807E-2(2) 2.20341E-2(2)

K

3 1.10128E-1(2) 4.40661E-2(2) 8.77730E-2(3) 3.51520E-2(3)

K

4 3.08188E-1(2) 1.23375E-1(2) 1.54206E-1(2) 6.16949E-2(2)

K

5 3.80688E-1(4) 2.19989E-1(3) 1.96149E-1(4) 1.20893E-1(2)

K

6 5.45362E-1(3) 2.41735E-1(2) 3.02120E-1(2) 1.94214E-1(4)

K

7 6.03433E-1(2) 3.77117E-1(4) 4.99295E-1(2) 1.99838E-1(2)

K

8 9.96464E-1(2) 3.99538E-1(2) 5.45362E-1(3) 2.19989E-1(3)

表九 旋轉傾斜梁不同設定角不同轉速的振動頻率 (橢圓斷面a b=5，

L

_T

a = 20

，

r = 0

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99916E-5 1.24880E-3 4.98287E-3 4.99916E-5 1.24877E-3 4.98245E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 3.33326E-5 8.32918E-4 3.32673E-3 3.33326E-5 8.32888E-4 3.32628E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.40395E-4 8.43072E-3 3.27386E-2 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 6.30781E-4 1.55520E-2 5.96020E-2

K1 1.75790E-2(B1) 1.81074E-2(B1) 2.52127E-2(B1) 3.36926E-2(B1) 1.87787E-2(B1) 3.36467E-2(B1) 4.86535E-2(B1) K2 8.77730E-2(C1) 8.84493E-2(C1) 1.03309E-1(C1) 1.39492E-1(C1) 8.83085E-2(C1) 1.00862E-1(3 C1) 1.34957E-1(C1) K 3 1.10128E-1(B2) 1.12588E-1(B2) 1.60565E-1(B2) 2.56707E-1(B2) 1.12699E-1(B2) 1.62529E-1(B2) 2.61795E-1(B2) K4 3.08188E-1(B3) 3.10910E-1(B3) 3.69635E-1(B3) 3.82522E-1(D1) 3.10951E-1(B3) 3.70494E-1(B3) 3.89135E-1(D1) K 5 3.80688E-1(D1) 3.80706E-1(D1) 3.81140E-1(D1) 5.07252E-1(B3) 3.80767E-1(D1) 3.82706E-1(D1) 5.09711E-1(B3) K 6 5.45362E-1(C2) 5.45960E-1(C2) 5.60134E-1(C2) 6.02264E-1(C2) 5.45935E-1(C2) 5.59518E-1(C2) 6.00133E-1(C2) K 7 6.03433E-1(B4) 6.06330E-1(B4) 6.71598E-1(B4) 8.39250E-1(B4) 6.06351E-1(B4) 6.72080E-1(B4) 8.40872E-1(B4) K 8 9.96464E-1(B5) 9.99459E-1(B5) 1.06850E+0(B5) 1.17327E+0(D2) 9.99472E-1(B5) 1.06879E+0(B5) 1.17544E+0(D2)

表十 旋轉傾斜梁不同設定角不同轉速的振動頻率 (橢圓斷面a b=5，

L

_T

a = 20

，

r = 0

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99915E-5 1.24876E-3 4.98234E-3 4.99916E-5 1.24880E-3 4.98287E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 3.33326E-5 8.32878E-4 3.32616E-3 3.33326E-5 8.32918E-4 3.32673E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 3.92926E-4 9.65654E-3 3.66375E-2 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 7.28157E-4 1.78328E-2 6.69863E-2 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.75790E-2(B1) 1.94310E-2(B1) 4.10871E-2(B1) 6.17458E-2(B1) 2.06859E-2(B1) 5.60149E-2(B1) 9.68849E-2(C1) K2 8.77730E-2(C1) 8.81666E-2(C1) 9.80516E-2(C1) 1.29439E-1(C1) 8.78792E-2( C1) 9.03238E-2(C1) 1.05599E-1(B1) K 3 1.10128E-1(B2) 1.12810E-1( B2) 1.64455E-1(B2) 2.66634E-1(B2) 1.13032E-1(B2) 1.68199E-1(B2) 2.75699E-1(B2) K4 3.08188E-1(B3) 3.10991E-1(B3 3.71345E-1(B3) 3.95221E-1(D1) 3.11072E-1(B3) 3.73024E-1(B3) 4.06117E-1(D1) K 5 3.80688E-1(D1) 3.80829E-1(D1) 3.84239E-1(D1) 5.12166E-1(B3) 3.80951E-1(D1) 3.87216E-1(D1) 5.17165E-1(B3) K 6 5.45362E-1(C2) 5.45910E-1(C2) 5.58902E-1(C2) 5.97895E-1(C2) 5.45859E-1(C2) 5.57669E-1(C2) 5.93048E-1(C2) K 7 6.03433E-1(B4) 6.06372E-1(B4) 6.72553E-1(B4) 8.42415E-1(B4) 6.06413E-1(B4) 6.73476E-1(B4) 8.45304E-1(B4) K 8 9.96464E-1(B5) 9.99485E-1(B5) 1.06909E+0(B5) 1.17749E+0(D2) 9.99510E-1(B5) 1.06968E+0(B5) 1.18128E+0(D2)

表十一 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 20

，

r = 1

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48965E-4 3.70759E-3 1.46317E-2 1.48965E-4 3.70757E-3 1.46313E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 8.33234E-5 2.07724E-3 8.23802E-3 8.33233E-5 2.07721E-3 8.23766E-3 V_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 W_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.40011E-4 8.20333E-3 2.96440E-2 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 6.29790E-4 1.49751E-2 5.20756E-2

K1 1.75790E-2(B1) 2.20016E-2(B1) 6.61208E-2(B1) 1.25028E-1(B1) 2.25575E-2(B1) 6.98042E-2(B1) 1.30086E-1(B1) K2 8.77730E-2(C1) 8.93364E-2(C1) 1.20774E-1(C1) 1.86628E-1(C1) 8.91969E-2(C1) 1.18671E-1(C1) 1.83113E-1(C1) K 3 1.10128E-1(B2) 1.16361E-1(B2) 2.16046E-1(B2) 3.82269E-1(B2) 1.16469E-1(B2) 2.17517E-1(B2) 3.85745E-1(B2) K4 3.08188E-1(B3) 3.14890E-1(B3) 3.86723E-1(D1) 4.03787E-1(D1) 3.14930E-1(B3) 3.88263E-1(D1) 4.09992E-1(D1) K 5 3.80688E-1(D1) 3.80933E-1(D1) 4.42653E-1(B3) 6.69713E-1(C2) 3.80994E-1(D1) 4.43371E-1(B3) 6.66850E-1(C2) K 6 5.45362E-1(C2) 5.46756E-1(C2) 5.79153E-1(C2) 6.90659E-1(B3) 5.46731E-1(C2) 5.78561E-1(C2) 6.93383E-1(B3) K 7 6.03433E-1(B4) 6.10554E-1(B4) 7.58255E-1(B4) 1.07846E+0(B4) 6.10575E-1(B4) 7.58681E-1(B4) 1.07971E+0(B4) K 8 9.96464E-1(B5) 1.00384E+0(B5) 1.16409E+0(D2) 1.21910E+0(D2) 1.00385E+0(B5) 1.16453E+0(D2) 1.22117E+0(D2)

表十二 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 20

，

r = 1

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48965E-4 3.70756E-3 1.46312E-2 1.48965E-4 3.70759E-3 1.46317E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 8.33233E-5 2.07720E-3 8.23757E-3 8.33234E-5 2.07724E-3 8.23802E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 3.92482E-4 9.39812E-3 3.32757E-2 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 7.27014E-4 1.71746E-2 5.86918E-2 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.75790E-2(B1) 2.31034E-2(B1) 7.37088E-2(B1) 1.35802E-1(B1) 2.41686E-2(B1) 8.29961E-2(B1) 1.56664E-1(C1) K2 8.77730E-2(C1) 8.90564E-2(C1) 1.16273E-1(C1) 1.78882E-1(C1) 8.87719E-2(C1) 1.09809E-1(C1) 1.60840E-1(B1) K 3 1.10128E-1(B2) 1.16576E-1(B2) 2.18966E-1(B2) 3.89094E-1(B2) 1.16791E-1(B2) 2.21804E-1(B2 3.95471E-1(B2) K4 3.08188E-1(B3) 3.14969E-1(B3) 3.89773E-1(D1) 4.15751E-1(D1)) 3.15049E-1(B3) 3.92705E-1(D1) 4.26168E-1(D1) K 5 3.80688E-1(D1) 3.81055E-1(D1)) 4.44084E-1(B3) 6.64668E-1 C2) 3.81178E-1(D1) 4.45501E-1(B3) 6.61325E-1(C2)) K 6 5.45362E-1(C2) 5.46706E-1(C2) 5.77965E-1(C2) 6.95356E-1(B3) 5.46655E-1(C2) 5.76763E-1(C2)) 6.98096E-1 (B3) K 7 6.03433E-1(B4) 6.10595E-1 (B4) 7.59102E-1(B4) 1.08092E+0(B4) 6.10637E-1(B4) 7.59927E-1(B4) 1.08326E+0(B4) K 8 9.96464E-1(B5) 1.00386E+0(B5) 1.16483E+0(D2) 1.22314E+0(D2) 1.00389E+0(B5) 1.16538E+0(D2) 1.22681E+0(D2)

表十三 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 20

，

r = 1

，

α = 30

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.35377E-6 3.20420E-5 1.15218E-4 1.35462E-6 3.25309E-5 1.20975E-4 εb 0.00000E+0 -9.96483E-5 -2.30394E-3 -7.58866E-3 -8.62386E-5 -1.96618E-3 -6.31707E-3 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.00186E-5 2.60022E-4 1.09899E-3 Utip 0.00000E+0 -2.76858E-6 -1.72345E-3 -1.49246E-2 -1.88212E-6 -1.24596E-3 -1.02717E-2

Vtip 0.00000E+0 -2.48731E-3 -5.53072E-2 -1.62563E-1 -2.15239E-3 -4.71186E-2 -1.35106E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 5.01055E-5 1.31674E-3 5.93775E-3

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.55361E-6 -3.99785E-4 -5.43601E-3 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.99927E-6 -1.71382E-3 -2.15568E-2

K1 1.75790E-2(B1) 1.76232E-2(B1) 1.86809E-2(B1) 2.17995E-2( B1) 1.76303E-2(B1) 1.88364E-2(B1) 2.22310E-2(B1) K2 8.77730E-2(C1) 8.77865E-2(C1) 8.76270E-2(C1) 8.54339E-2(C1) 8.77853E-2(C1) 8.77307E-2(C1) 8.64040E-2(C1) K 3 1.10128E-1(B2) 1.10187E-1(B2) 1.11562E-1(B2) 1.15708E-1(B2) 1.10188E-1(B2) 1.11595E-1(B2) 1.15827E-1(B2) K4 3.08188E-1(B3) 3.08250E-1(B3) 3.09508E-1( B3) 3.12485E-1(B3) 3.08251E-1(B3) 3.09578E-1(B3) 3.13035E-1 B3) K 5 3.80688E-1(D1) 3.80692E-1(D1) 3.81584E-1(D1) 3.87563E-1(D1) 3.80692E-1(D1) 3.81374E-1(D1) 3.85782E-1(D1) K 6 5.45362E-1(C2) 5.45376E-1(C2) 5.46297E-1(C2) 5.50333E-1(C2) 5.45375E-1(C2) 5.46117E-1(C2) 5.49012E-1(C2) K 7 6.03433E-1(B4) 6.03498E-1(B4) 6.04733E-1(B4) 6.06968E-1(B4) 6.03499E-1(B4) 6.04830E-1(B4) 6.07858E-1(B4) K 8 9.96464E-1(B5) 9.96531E-1(B5) 9.97599E-1(B5) 9.98173E-1(B5) 9.96531E-1(B5) 9.97752E-1(B5) 9.99618E-1(B5)

表十四 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 20

，

r = 1

，

α = 30

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.35546E-6 3.29929E-5 1.26027E-4 1.35715E-6 3.38428E-5 1.34325E-4 εb 0.00000E+0 -7.03651E-5 -1.58235E-3 -4.96363E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 1.41587E-5 3.62431E-4 1.49796E-3 1.99959E-5 4.98220E-4 1.97227E-3 Utip 0.00000E+0 -9.98432E-7 -7.98233E-4 -6.28402E-3 7.60623E-7 1.56177E-5 2.17177E-5 Vtip 0.00000E+0 -1.75605E-3 -3.78545E-2 -1.05887E-1 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 7.08052E-5 1.82623E-3 7.84248E-3 9.99794E-5 2.48719E-3 9.79759E-3

) 1

1(

Θ 0.00000E+0 2.95027E-6 -4.42438E-4 -5.70206E-3 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 3.46939E-6 -1.90693E-3 -2.27383E-2 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.75790E-2(B1) 1.76374E-2 B1 1.89920E-2(B1) 2.26926E-2(B1) 1.76515E-2(B1) 1.93034E-2(B1) 2.36770E-2(B1) K2 8.77730E-2(C1) 8.77841E-2(C1) 8.78261E-2(C1) 8.72641E-2(C1) 8.77818E-2(C1) 8.79942E-2(C1) 8.86576E-2(C1) K 3 1.10128E-1(B2) 1.10189E-1(B2) 1.11627E-1(B2) 1.15934E-1(B2) 1.10191E-1(B2) 1.11691E-1(B2) 1.16130E-1(B2) K4 3.08188E-1(B3) 3.08251E-1(B3) 3.09645E-1(B3) 3.13506E-1(B3) 3.08252E-1(B3) 3.09768E-1(B3) 3.14250E-1(B3) K 5 3.80688E-1(D1) 3.80692E-1(D1) 3.81174E-1(D1) 3.84119E-1(D1) 3.80692E-1(D1) 3.80807E-1(D1) 3.81220E-1(D1) K 6 5.45362E-1(C2) 5.45375E-1(C2) 5.45951E-1(C2) 5.47969E-1(C2) 5.45374E-1(C2) 5.45658E-1(C2) 5.46543E-1(C2) K 7 6.03433E-1(B4) 6.03499E-1(B4) 6.04921E-1(B4) 6.08631E-1(B4) 6.03500E-1(B4) 6.05089E-1( B4) 6.09886E-1(B4) K 8 9.96464E-1(B5) 9.96532E-1(B5) 9.97897E-1 (B5) 1.00091E+0(B5) 9.96532E-1(B5) 9.98165E-1(B5) 1.00308E+0(B5)

表十五 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 20

，

r = 1

，

α = 45

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.19290E-6 2.61192E-5 7.63258E-5 1.19460E-6 2.71223E-5 8.83053E-5 εb 0.00000E+0 -1.41013E-4 -3.30020E-3 -1.10637E-2 -1.22037E-4 -2.81657E-3 -9.22070E-3 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.41688E-5 3.67753E-4 1.54466E-3 Utip 0.00000E+0 -6.39456E-6 -3.58478E-3 -3.23073E-2 -4.61872E-6 -2.60007E-3 -2.25360E-2

Vtip 0.00000E+0 -3.52044E-3 -7.94579E-2 -2.37516E-1 -3.04641E-3 -6.77321E-2 -1.98835E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 7.08636E-5 1.88169E-3 9.05387E-3

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.70054E-6 -9.02483E-4 -1.17678E-2 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -3.18745E-7 -3.65668E-3 -4.59744E-2

K1 1.75790E-2(B1) 1.76162E-2(B1) 1.85471E-2(B1) 2.15400E-2(B1) 1.76233E-2(B1) 1.86923E-2(B1) 2.18337E-2(B1) K2 8.77730E-2(C1) 8.77840E-2(C1) 8.70568E-2(C1) 8.15341E-2(C1) 8.77831E-2(C1) 8.73032E-2(C1) 8.33765E-2(C1) K 3 1.10128E-1(B2) 1.10180E-1(B2) 1.11376E-1(B2) 1.14923E-1(B2) 1.10181E-1(B2) 1.11415E-1(B2) 1.15088E-1(B2) K4 3.08188E-1(B3) 3.08243E-1(B3) 3.09095E-1(B3) 3.09726E-1(B3) 3.08244E-1(B3) 3.09230E-1(B3) 3.10844E-1(B3) K 5 3.80688E-1(D1) 3.80693E-1(D1) 3.82438E-1(D1) 3.93099E-1(D1) 3.80693E-1(D1) 3.82003E-1(D1) 3.90302E-1(D1) K 6 5.45362E-1(C2) 5.45376E-1(C2) 5.46940E-1(C2) 5.55173E-1(C2) 5.45375E-1(C1) 5.46569E-1(C1) 5.52174E-1(C1) K 7 6.03433E-1(B4) 6.03491E-1(B4) 6.04198E-1(B4) 6.03024E-1(B4) 6.03491E-1(B4) 6.04390E-1(B4) 6.04824E-1(B4) K 8 9.96464E-1(B5) 9.96523E-1(B5) 9.96831E-1(B5) 9.92334E-1(B5) 9.96523E-1(B5) 9.97139E-1(B5) 9.95047E-1(B5)

表十六 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 20

，

r = 1

，

α = 45

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.19630E-6 2.80717E-5 9.90937E-5 1.19968E-6 2.98215E-5 1.17201E-4 εb 0.00000E+0 -9.95740E-5 -2.26677E-3 -7.24628E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 2.00239E-5 5.12711E-4 2.11408E-3 2.82791E-5 7.05037E-4 2.79612E-3 Utip 0.00000E+0 -2.84845E-6 -1.67498E-3 -1.39399E-2 6.75441E-7 1.00792E-5 -4.18430E-5

Vtip 0.00000E+0 -2.48544E-3 -5.44415E-2 -1.56666E-1 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 1.00138E-4 2.60107E-3 1.16687E-2 1.41397E-4 3.52028E-3 1.38997E-2

) 1

1(

Θ 0.00000E+0 1.96687E-6 -1.00350E-3 -1.24797E-2 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 -3.55770E-7 -4.07742E-3 -4.89149E-2 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.75790E-2(B1) 1.76303E-2(B1) 1.88391E-2(B1) 2.21979E-2(B1) 1.76444E-2(B1) 1.91366E-2(B1) 2.30887E-2(B1) K2 8.77730E-2(C1) 8.77822E-2(C1) 8.75353E-2(C1) 8.51801E-2(C1) 8.77804E-2(C1) 8.79588E-2(C1) 8.85211E-2(C1) K 3 1.10128E-1(B2) 1.10183E-1(B2) 1.11453E-1(B2) 1.15214E-1(B2) 1.10185E-1(B2) 1.11526E-1(B2) 1.15369E-1(B2) K4 3.08188E-1(B3) 3.08245E-1(B3) 3.09357E-1(B3) 3.11821E-1(B3) 3.08246E-1(B3) 3.09590E-1(B3) 3.13348E-1(B3) K 5 3.80688E-1(D1) 3.80693E-1(D1) 3.81586E-1(D1) 3.87310E-1(D1) 3.80692E-1(D1) 3.80802E-1(D1) 3.81255E-1(D1) K 6 5.45362E-1(C1) 5.45374E-1(C1) 5.46228E-1(C1) 5.49745E-1(C1) 5.45372E-1(C1) 5.45626E-1(C1) 5.46410E-1(C1) K 7 6.03433E-1(B4) 6.03492E-1(B4) 6.04572E-1(B4) 6.06409E-1(B4) 6.03493E-1(B4) 6.04908E-1(B4) 6.09026E-1(B4) K 8 9.96464E-1(B5) 9.96524E-1(B5) 9.97432E-1(B5) 9.97605E-1(B5) 9.96525E-1(B5) 9.97976E-1(B5) 1.00216E+0(B5)

表十七 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，L_T a=50，

r = 0

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99917E-5 1.24880E-3 4.98287E-3 4.99917E-5 1.24879E-3 4.98274E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 3.33327E-5 8.32918E-4 3.32673E-3 3.33327E-5 8.32913E-4 3.32666E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.46642E-4 8.58448E-3 3.33250E-2 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 6.31907E-4 1.55805E-2 5.97221E-2

K1 7.03196E-3(B1) 8.14778E-3( B1) 1.49966E-2( B1) 2.07795E-2( B1) 9.48067E-3( B1) 2.16995E-2( B1) 2.98642E-2( B1) K2 3.51520E-2(C1) 3.68086E-2( C1) 6.44927E-2( C1) 1.12037E-1( C1) 3.64877E-2( C1) 6.25437E-2( C1) 1.09926E-1( C1) K 3 4.40661E-2(B2) 4.98992E-2( B2) 1.23658E-1(B2) 2.32394E-1( B2) 5.01490E-2(B2) 1.26114E-1( B2) 2.37341E-1( B2) K4 1.23375E-1( B3) 1.30010E-1( B3) 2.35107E-1( B3) 3.35925E-1( C2) 1.30106E-1( B3) 2.36441E-1 (B3) 3.32541E-1( C2) K 5 2.19989E-1(C2) 2.21456E-1( C2) 2.54139E-1( C2) 3.79481E-1( D1) 2.21399E-1( C2) 2.52948E-1 (C2) 3.85969E-1( D1) K 6 2.41735E-1(B4) 2.48867E-1( B4) 3.77378E-1( B4) 4.09463E-1( B3) 2.48918E-1( B4) 3.78221E-1( B4) 4.12787E-1( B3) K 7 3.77117E-1(D1) 3.77139E-1( D1) 3.77660E-1 (D1) 6.12049E-1( B4) 3.77200E-1(D1) 3.79216E-1( D1) 6.14193E-1( B4) K 8 3.99538E-1(B5) 4.06946E-1( B5) 5.52088E-1( B5) 7.44543E-1(C3) 4.06977E-1( B5) 5.52665E-1( B5 7.42787E-1(C3)

表十八 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，L_T a=50，

r = 0

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99917E-5 1.24878E-3 4.98270E-3 4.99917E-5 1.24880E-3 4.98287E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 3.33327E-5 8.32911E-4 3.32664E-3 3.33327E-5 8.32918E-4 3.32673E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 4.00135E-4 9.83108E-3 3.72720E-2 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 7.29453E-4 1.78620E-2 6.70744E-2 0.00000E+0 0.00000E+0 0.00000E+0

K1 7.03196E-3(B1) 1.06911E-2(B1) 2.74882E-2(B1) 3.72163E-2(B1) 1.28993E-2(B1) 4.06850E-2(C1) 5.02236E-2(C1) K2 3.51520E-2(C1) 3.61513E-2(C1) 6.02160E-2(C1) 1.07629E-1(C1) 3.54229E-2(C1) 5.22084E-2(B1) 1.02168E-1(B1) K 3 4.40661E-2(B2) 5.03976E-2(B2) 1.28554E-1(B2) 2.42386E-1(B2) 5.08917E-2(B2) 1.33409E-1(B2) 2.53185E-1(B2) K4 1.23375E-1(B3) 1.30202E-1(B3) 2.37760E-1(B3) 3.28950E-1(C2) 1.30394E-1(B3) 2.40383E-1(B3) 3.20819E-1(C2) K 5 2.19989E-1(C2) 2.21342E-1(C2) 2.51725E-1(C2) 3.91964E-1(D1) 2.21229E-1(C2) 2.49154E-1(C2) 4.02701E-1(D1) K 6 2.41735E-1(B4) 2.48968E-1(B4) 3.79055E-1(B4) 4.15901E-1(B3) 2.49068E-1(B4) 3.80689E-1(B4) 4.21634E-1(B3) K 7 3.77117E-1(D1) 3.77261E-1(D1) 3.80738E-1(D1) 6.16269E-1(B4) 3.77382E-1(D1) 3.83688E-1(D1) 6.20270E-1(B4) K 8 3.99538E-1(B5) 4.07008E-1(B5) 5.53235E-1(B5) 7.41062E-1(C3) 4.07069E-1(B5) 5.54359E-1(B5) 7.37661E-1(C3)

表十九 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，L_T a=50，

r = 1

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48966E-4 3.70759E-3 1.46316E-2 1.48966E-4 3.70758E-3 1.46315E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 8.33235E-5 2.07724E-3 8.23801E-3 8.33235E-5 2.07723E-3 8.23795E-3 V_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 W_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.46241E-4 8.34820E-3 3.01183E-2 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 6.30908E-4 1.50000E-2 5.21531E-2

K1 7.03196E-3(B1) 1.48226E-2(B1) 6.24807E-2(B1) 1.21737E-1(B1) 1.55954E-2(B1) 6.45234E-2(B1) 1.23819E-1(B1) K2 3.51520E-2(C1) 3.88823E-2(C1) 8.93792E-2(C1) 1.65751E-1(C1) 3.85786E-2(C1) 8.79103E-2(C1) 1.64184E-1(C1) K 3 4.40661E-2(B2) 5.78497E-2(B2) 1.87755E-1(B2) 3.63111E-1(B2) 5.80653E-2(B2) 1.89389E-1(B2) 3.66376E-1(B2) K4 1.23375E-1(B3) 1.39150E-1(B3) 2.93219E-1(C2) 4.00138E-1(C2) 1.39240E-1(B3) 2.92162E-1(C2) 4.06406E-1(D1) K 5 2.19989E-1(C2) 2.23401E-1(C2) 3.30263E-1(B3) 4.43566E-1(D1) 2.23345E-1(C2) 3.31239E-1(B3) 4.40794E-1(C2) K 6 2.41735E-1(B4) 2.58908E-1(B4) 3.83312E-1(D1) 6.06635E-1(B3) 2.58956E-1(B4) 3.84838E-1(D1) 6.08905E-1(B3) K 7 3.77117E-1(D1) 3.77368E-1(D1) 5.04091E-1(B4) 8.80545E-1(B4) 3.77429E-1(D1) 5.04724E-1(B4) 8.80614E-1(B4) K 8 3.99538E-1(B5) 4.17534E-1(B5) 6.95459E-1(C3) 8.88939E-1(C3) 4.17564E-1(B5) 6.94979E-1(C3) 8.88903E-1(B5)

表二十 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 50

，

r = 1

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48966E-4 3.70758E-3 1.46315E-2 1.48966E-4 3.70759E-3 1.46316E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 8.33235E-5 2.07723E-3 8.23794E-3 8.33235E-5 2.07724E-3 8.23801E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 3.99672E-4 9.56270E-3 3.37922E-2 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 7.28299E-4 1.72003E-2 5.87462E-2 0.00000E+0 0.00000E+0 0.00000E+0

K1 7.03196E-3(B1) 1.63597E-2(B1) 6.68286E-2(B1) 1.26050E-1(B1) 1.78813E-2(B1) 7.39603E-2(C1) 1.31233E-1(C1) K2 3.51520E-2(C1) 3.82604E-2(C1) 8.61658E-2(C1) 1.62459E-1(C1) 3.75728E-2(C1) 8.01186E-2(B1) 1.58266E-1 (B1) K 3 4.40661E-2(B2) 5.82802E-2(B2) 1.91030E-1(B2) 3.69733E-1(B2) 5.87081E-2(B2) 1.94342E-1(B2) 3.76956E-1(B2) K4 1.23375E-1(B3) 1.39330E-1(B3) 2.91092E-1(C2) 4.12223E-1(C2) 1.39509E-1(B3) 2.88906E-1(C2) 4.22930E-1(D1) K 5 2.19989E-1(C2) 2.23289E-1(C2) 3.32195E-1(B3) 4.37902E-1(D1) 2.23176E-1(C2) 3.34055E-1(B3) 4.31344E-1(C2) K 6 2.41735E-1(B4) 2.59005E-1(B4) 3.86334E-1(D1) 6.11052E-1(B3) 2.59101E-1(B4) 3.89237E-1(D1) 6.15040E-1(B3) K 7 3.77117E-1(D1) 3.77490E-1(D1) 5.05351E-1(B4) 8.80982E-1(B4) 3.77612E-1(D1) 5.06586E-1(B4) 8.83118E-1(C3) K 8 3.99538E-1(B5) 4.17594E-1(B5) 6.94515E-1(C3) 8.88546E-1(B5) 4.17654E-1(B5) 6.93627E-1(C3) 8.86370E-1(B4)

表二十一 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 50

，

r = 1

，

α = 30

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.33600E-6 2.75260E-5 9.80188E-5 1.34123E-6 2.92328E-5 1.01767E-4 εb 0.00000E+0 -2.44706E-4 -4.24689E-3 -1.04761E-2 -2.11044E-4 -3.50077E-3 -8.36830E-3 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.52875E-5 6.98179E-4 2.65744E-3 Utip 0.00000E+0 -1.30091E-4 -2.52333E-2 -6.81571E-2 -9.65084E-5 -1.71579E-2 -4.73763E-2

Vtip 0.00000E+0 -1.51400E-2 -2.11052E-1 -3.48922E-1 -1.30503E-2 -1.74226E-1 -2.89261E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.16749E-4 9.91402E-3 4.18888E-2

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -3.10196E-5 -1.22743E-2 -6.57466E-2 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -1.20096E-4 -4.42347E-2 -2.37723E-1

K1 7.03196E-3(B1) 7.14250E-3(B1) 9.56371E-3(B1) 1.47557E-2(B1) 7.15968E-3(B1) 9.77384E-3(B1) 1.49293E-2(B1) K2 3.51520E-2(C1) 3.51713E-2(C1) 3.35470E-2(C1) 3.44561E-2(C1) 3.51722E-2(C1) 3.41820E-2(C1) 3.50145E-2(C1) K 3 4.40661E-2(B2) 4.42121E-2(B2) 4.75376E-2(B2) 5.73517E-2(B2) 4.42151E-2(B2) 4.75926E-2(B2) 5.70529E-2(B2) K4 1.23375E-1(B3) 1.23524E-1(B3) 1.26058E-1(B3) 1.36212E-1(B3) 1.23527E-1(B3) 1.26399E-1(B3) 1.36328E-1(B3) K 5 2.19989E-1(C2) 2.19966E-1(C2) 2.15239E-1(C2) 2.17484E-1(C2) 2.19979E-1(C2) 2.16937E-1(C2) 2.18626E-1(C2) K 6 2.41735E-1(B4) 2.41890E-1(B4) 2.44000E-1(B4) 2.52989E-1(B4) 2.41893E-1(B4) 2.44539E-1(B4) 2.54218E-1(B4) K 7 3.77117E-1(D1) 3.77314E-1(D1) 4.01253E-1(D1) 4.06084E-1(D1) 3.77264E-1(D1) 3.93756E-1(D1) 3.98077E-1(D1) K 8 3.99538E-1(B5) 3.99697E-1(B5) 4.01351E-1(B5) 4.08776E-1(B5) 3.99700E-1(B5) 4.02054E-1(B5) 4.10298E-1(B5)

表二十二 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 50

，

r = 1

，

α = 30

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.34637E-6 3.07908E-5 1.09500E-4 1.35641E-6 3.33988E-5 1.28155E-4 εb 0.00000E+0 -1.71608E-4 -2.72439E-3 -6.29968E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 3.56141E-5 9.44307E-4 3.60411E-3 4.99533E-5 1.22349E-3 4.60742E-3 Utip 0.00000E+0 -6.35511E-5 -1.03780E-2 -2.89780E-2 5.43647E-7 -1.11719E-4 -1.66580E-3

Vtip 0.00000E+0 -1.06059E-2 -1.35474E-1 -2.23772E-1 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 4.45738E-4 1.27284E-2 5.14649E-2 6.24203E-4 1.51393E-2 5.53005E-2

) 1

1(

Θ 0.00000E+0 -3.54274E-5 -1.27417E-2 -6.85497E-2 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 -1.37272E-4 -4.59872E-2 -2.49484E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 7.03196E-3(B1) 7.17684E-3(B1) 1.00174E-2(B1) 1.53643E-2(B1) 7.21108E-3(B1) 1.05717E-2(B1) 1.69385E-2(B1) K2 3.51520E-2(C1) 3.51729E-2(C1) 3.47598E-2(C1) 3.57478E-2(C1) 3.51741E-2(C1) 3.57047E-2(C1) 3.73553E-2(C1) K 3 4.40661E-2(B2) 4.42181E-2(B2) 4.76390E-2(B2) 5.67525E-2(B2) 4.42241E-2(B2) 4.77195E-2(B2) 5.62321E-2(B2) K4 1.23375E-1(B3) 1.23530E-1(B3) 1.26688E-1(B3) 1.36389E-1(B3) 1.23535E-1(B3) 1.27133E-1(B3) 1.36280E-1(B3) K 5 2.19989E-1(C2) 2.19993E-1(C2) 2.18428E-1(C2) 2.20111E-1(C2) 2.20018E-1(C2) 2.20720E-1(C2) 2.22858E-1(C2) K 6 2.41735E-1(B4) 2.41896E-1(B4) 2.44990E-1(B4) 2.54984E-1(B4) 2.41901E-1(B4) 2.45682E-1(B4) 2.55470E-1(B4) K 7 3.77117E-1(D1) 3.77216E-1(D1) 3.87218E-1(D1) 3.89679E-1(D1) 3.77122E-1(D1) 3.77067E-1(D1) 3.75546E-1(D1) K 8 3.99538E-1(B5) 3.99703E-1(B5) 4.02661E-1(B5) 4.11736E-1(B5) 3.99709E-1(B5) 4.03640E-1(B5) 4.14233E-1(B5)

表二十三 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 50

，

r = 1

，

α = 45

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.15705E-6 1.62012E-5 3.72887E-5 1.16759E-6 1.94607E-5 3.06731E-5 εb 0.00000E+0 -3.47369E-4 -6.22357E-3 -1.54730E-2 -2.99585E-4 -5.14133E-3 -1.23155E-2 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.57671E-5 9.76901E-4 3.49768E-3 Utip 0.00000E+0 -2.63589E-4 -5.50951E-2 -1.50473E-1 -1.95776E-4 -3.84054E-2 -1.14872E-1

Vtip 0.00000E+0 -2.15137E-2 -3.08943E-1 -5.05796E-1 -1.85449E-2 -2.58676E-1 -4.38825E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 4.48404E-4 1.58849E-2 7.42017E-2

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -6.58457E-5 -2.60002E-2 -1.39902E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -2.47877E-4 -9.40535E-2 -5.16324E-1

K1 7.03196E-3(B1) 7.12598E-3(B1) 9.45741E-3(B1) 1.46710E-2(B1) 7.14291E-3(B1) 9.55317E-3(B1) 1.42799E-2(B1) K2 3.51520E-2(C1) 3.51505E-2(C1) 3.11764E-2(C1) 3.11993E-2(C1) 3.51558E-2(C1) 3.22197E-2(C1) 3.12878E-2(C1) K 3 4.40661E-2(B2) 4.41956E-2(B2) 4.70933E-2(B2) 5.67247E-2(B2) 4.41988E-2(B2) 4.71709E-2(B2) 5.63080E-2(B2) K4 1.23375E-1(B3) 1.23501E-1(B3) 1.24353E-1(B3) 1.32727E-1(B3) 1.23505E-1(B3) 1.25023E-1(B3) 1.32932E-1(B3) K 5 2.19989E-1(C2) 2.19907E-1(C2) 2.09623E-1(C2) 2.10622E-1(C2) 2.19935E-1(C2) 2.12462E-1(C2) 2.10397E-1(C2) K 6 2.41735E-1(B4) 2.41864E-1(B4) 2.41619E-1(B4) 2.46678E-1(B4) 2.41869E-1(B4) 2.42702E-1(B4) 2.49725E-1(B4) K 7 3.77117E-1(D1) 3.77512E-1(D1) 3.98403E-1(B5) 4.00392E-1(B5) 3.77411E-1(D1) 3.99684E-1(B5) 4.02550E-1(B5) K 8 3.99538E-1(B5) 3.99668E-1(B5) 4.25157E-1(D1) 4.30621E-1(D1) 3.99674E-1(B5) 4.12408E-1(D1) 4.24360E-1(D1)

表二十四 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=5，

L

_T

a = 50

，

r = 1

，

α = 45

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.17796E-6 2.27934E-5 4.24443E-5 1.19819E-6 2.89254E-5 1.04470E-4 εb 0.00000E+0 -2.43602E-4 -4.00064E-3 -9.08062E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 5.03735E-5 1.33102E-3 4.91702E-3 7.06559E-5 1.73678E-3 6.59985E-3 Utip 0.00000E+0 -1.29217E-4 -2.36237E-2 -7.62299E-2 2.41305E-7 -2.47147E-4 -3.53304E-3

Vtip 0.00000E+0 -1.50718E-2 -2.03203E-1 -3.54294E-1 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 6.30834E-4 1.96444E-2 8.96161E-2 8.82937E-4 2.15128E-2 7.94495E-2

) 1

1(

Θ 0.00000E+0 -7.52481E-5 -2.74577E-2 -1.61437E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 -2.83410E-4 -9.93998E-2 -6.00452E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 7.03196E-3(B1) 7.15983E-3(B1) 9.71932E-3(B1) 1.41805E-2(B1) 7.19362E-3(B1) 1.02199E-2(B1) 1.57010E-2(B1) K2 3.51520E-2(C1) 3.51608E-2(C1) 3.33375E-2(C1) 3.19015E-2(C1) 3.51705E-2(C1) 3.56220E-2(C1) 3.70871E-2(C1) K 3 4.40661E-2(B2) 4.42019E-2(B2) 4.72176E-2(B2) 5.58113E-2(B2) 4.42083E-2(B2) 4.72111E-2(B2) 5.31819E-2(B2) K4 1.23375E-1(B3) 1.23510E-1(B3) 1.25626E-1(B3) 1.33291E-1(B3) 1.23519E-1(B3) 1.26569E-1(B3) 1.32462E-1(B3) K 5 2.19989E-1(C2) 2.19962E-1(C2) 2.15342E-1(C2) 2.12318E-1(C2) 2.20015E-1(C2) 2.20637E-1(C2) 2.22485E-1(C2) K 6 2.41735E-1(B4) 2.41874E-1(B4) 2.43635E-1(B4) 2.51924E-1(B4) 2.41884E-1(B4) 2.45080E-1(B4) 2.51289E-1(B4) K 7 3.77117E-1(D1) 3.77312E-1(D1) 3.99484E-1(B5) 4.05059E-1(B5) 3.77121E-1(D1) 3.76888E-1(D1) 3.73261E-1(D1) K 8 3.99538E-1(B5) 3.99680E-1(B5) 4.01155E-1(D1) 4.12710E-1 (D1) 3.99692E-1(B5) 4.03052E-1(B5) 4.10369E-1(B5)

表二十五 旋轉傾斜梁不同設定角不同轉速的振動頻率 (橢圓斷面

a b = 10

，

L

_T

a = 20

，

r = 0

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99917E-5 1.24880E-3 4.98287E-3 4.99911E-5 1.24846E-3 4.97847E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 3.33327E-5 8.32918E-4 3.32673E-3 3.33319E-5 8.32473E-4 3.32124E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.36033E-3 3.28706E-2 1.17467E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.52159E-3 5.99277E-2 2.05749E-1

K1 8.78991E-3(B1) 9.74415E-3(B1) 1.69165E-2(B1) 2.33216E-2(B1) 1.09424E-2(B1) 2.81364E-2(B1) 4.28833E-2(B1) K2 5.50807E-2(B2) 5.98499E-2(B2) 1.03268E-1(C1) 1.39183E-1(C1) 6.00589E-2(B2) 1.00747E-1(C1) 1.34544E-1(C1) K 3 8.77730E-2(C1) 8.84480E-2(C1) 1.28396E-1(B2) 1.98792E-1(D1) 8.83076E-2(C1) 1.31044E-1(B2) 2.14911E-1(D1) K4 1.54206E-1(B3) 1.59569E-1(B3) 1.96830E-1(D1) 2.35577E-1(B2) 1.59648E-1(B3) 2.00217E-1(D1) 2.42418E-1(B2) K 5 1.96149E-1(D1) 1.96176E-1(D1) 2.53723E-1(B3) 4.22739E-1(B3) 1.96301E-1(D1) 2.55021E-1(B3) 4.25438E-1(B3) K 6 3.02120E-1(B4) 3.07861E-1(B4) 4.19952E-1(B4) 6.00159E-1(C2) 3.07902E-1(B4) 4.20675E-1(B4) 5.97568E-1(C2) K 7 4.99295E-1(B5) 5.05245E-1(B5) 5.59590E-1(C2) 6.43780E-1(B4) 5.05270E-1(B5) 5.59230E-1(C2) 6.46703E-1(B4) K 8 5.45362E-1(C2) 5.45938E-1(C2) 6.04313E-1(D2) 6.44727E-1(D2) 5.45919E-1(C2) 6.05270E-1(D2) 6.50904E-1(D2)

表二十六 旋轉傾斜梁不同設定角不同轉速的振動頻率 (橢圓斷面a b=10，

L

_T

a = 20

，

r = 0

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99909E-5 1.24837E-3 4.97795E-3 4.99917E-5 1.24880E-3 4.98287E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 3.33317E-5 8.32360E-4 3.32080E-3 3.33327E-5 8.32918E-4 3.32673E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 1.56874E-3 3.67802E-2 1.21640E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 2.90842E-3 6.73444E-2 2.16355E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 8.78991E-3(B1) 1.20277E-2(B1) 3.67843E-2(B1) 5.78545E-2(B1) 1.39627E-2(B1) 5.27938E-2(B1) 9.68849E-2(C1) K2 5.50807E-2(B2) 6.02669E-2(B2) 9.79128E-2(C1) 1.28832E-1(C1) 6.06800E-2(B2) 9.03238E-2(C1) 1.02723E-1(B1) K 3 8.77730E-2(C1) 8.81660E-2(C1) 1.33469E-1(B2) 2.26473E-1(D1) 8.78792E-2(C1) 1.37813E-1(B2) 2.42829E-1(D1) K4 1.54206E-1(B3) 1.59727E-1(B3) 2.03322E-1(D1) 2.47757E-1(B2) 1.59883E-1(B3) 2.08851E-1(D1) 2.56115E-1(B2) K 5 1.96149E-1(D1) 1.96426E-1(D1) 2.56265E-1(B3) 4.28350E-1(B3) 1.96673E-1(D1) 2.58621E-1(B3) 4.34544E-1(B3) K 6 3.02120E-1(B4) 3.07942E-1(B4) 4.21414E-1(B4) 5.95845E-1(C2) 3.08024E-1(B4) 4.22933E-1(B4) 5.93048E-1(C2) K 7 4.99295E-1(B5) 5.05294E-1(B5) 5.58781E-1(C2) 6.49794E-1(B4) 5.05344E-1(B5) 5.57669E-1(C2) 6.51607E-1(B4) K 8 5.45362E-1(C2) 5.45899E-1(C2) 6.06172E-1(D2) 6.53336E-1(D2) 5.45859E-1(C2) 6.07834E-1(D2) 6.57734E-1(D2)

表二十七 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面

a b = 10

，

L

_T

a = 20

，

r = 1

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48966E-4 3.70759E-3 1.46317E-2 1.48965E-4 3.70732E-3 1.46293E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 8.33236E-5 2.07724E-3 8.23802E-3 8.33228E-5 2.07688E-3 8.23513E-3 V_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 W_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.35461E-3 2.98855E-2 8.81010E-2 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.50681E-3 5.26105E-2 1.40678E-1

K1 8.78991E-3(B1) 1.57866E-2(B1) 6.30411E-2(B1) 1.22265E-1(B1) 1.65533E-2(B1) 6.69659E-2(B1) 1.27694E-1(B1) K2 5.50807E-2(B2) 6.66460E-2(B2) 1.20727E-1(C1) 1.86247E-1(C1) 6.68337E-2(B2) 1.18588E-1(C1) 1.82760E-1(C1) K 3 8.77730E-2(C1) 8.93351E-2(C1) 1.91437E-1(B2) 2.36062E-1(D1) 8.91961E-2(C1) 1.93203E-1(B2) 2.48733E-1(D1) K4 1.54206E-1(B3) 1.67137E-1(B3) 2.07287E-1(D1) 3.65671E-1(B2) 1.67213E-1(B3) 2.10473E-1(D1) 3.69867E-1(B2) K 5 1.96149E-1(D1) 1.96615E-1(D1) 3.45849E-1(B3) 6.18589E-1(B3) 1.96739E-1(D1) 3.46777E-1(B3) 6.18358E-1(B3) K 6 3.02120E-1(B4) 3.16060E-1(B4) 5.40172E-1(B4) 6.68124E-1(C2) 3.16100E-1(B4) 5.40550E-1(B4) 6.69138E-1(C2) K 7 4.99295E-1(B5) 5.13830E-1(B5) 5.78669E-1(C2) 7.19769E-1(D2) 5.13854E-1(B5) 5.78505E-1(C2) 7.23400E-1(D2) K 8 5.45362E-1(C2) 5.46734E-1(C2) 6.26752E-1(D2) 9.09832E-1(B4) 5.46715E-1(C3) 6.27678E-1(D2) 9.11598E-1(B4)

表二十八 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=10，

L

_T

a = 20

，

r = 1

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48965E-4 3.70724E-3 1.46289E-2 1.48966E-4 3.70759E-3 1.46317E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 8.33225E-5 2.07679E-3 8.23474E-3 8.33236E-5 2.07724E-3 8.23802E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 1.56214E-3 3.35389E-2 9.37336E-2 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 2.89138E-3 5.92825E-2 1.51620E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 8.78991E-3(B1) 1.72900E-2(B1) 7.10672E-2(B1) 1.33769E-1(B1) 1.86882E-2(B1) 8.05577E-2(B1) 1.56664E-1(C1) K2 5.50807E-2(B2) 6.70207E-2(B2) 1.16174E-1(C1) 1.78417E-1(C1) 6.73925E-2(B2) 1.09809E-1(C1) 1.58677E-1(B1) K 3 8.77730E-2(C1) 8.90559E-2(C1) 1.94860E-1(B2) 2.58760E-1(D1) 8.87719E-2(C1) 1.97902E-1(B2) 2.74087E-1(D1) K4 1.54206E-1(B3) 1.67287E-1(B3) 2.13422E-1(D1) 3.73440E-1(B2) 1.67437E-1(B3) 2.18729E-1(D1) 3.79428E-1(B2) K 5 1.96149E-1(D1) 1.96864E-1(D1) 3.47689E-(B3) 6.19847E-1(B3) 1.97111E-1(D1) 3.49474E-1(B3) 6.26841E-1(B3) K 6 3.02120E-1(B4) 3.16140E-1(B4) 5.41069E-1(B4) 6.68077E-1(C2) 3.16219E-1(B4) 5.42503E-1(B4) 6.61325E-1(C1) K 7 4.99295E-1(B5) 5.13878E-1(B5) 5.78122E-1(C2) 7.26504E-1(D2) 5.13927E-1(B5) 5.76763E-1(C1) 7.31721E-1(D2) K 8 5.45362E-1(C2) 5.46695E-1(C2) 6.28555E-1(D2) 9.13075E-1(B4) 5.46655E-1(C1) 6.30185E-1(D2) 9.15479E-1(B4)

表二十九 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=10，

L

_T

a = 20

，

r = 1

，

α = 30

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.34346E-6 2.88072E-5 1.00973E-4 1.34694E-6 3.02793E-5 1.06909E-4 εb 0.00000E+0 -1.97260E-4 -3.79455E-3 -9.97337E-3 -1.70357E-4 -3.15161E-3 -7.96887E-3 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.00814E-5 2.79307E-4 1.16565E-3 Utip 0.00000E+0 -5.40739E-5 -1.49846E-2 -5.42850E-2 -4.01043E-5 -1.02640E-2 -3.60056E-2

Vtip 0.00000E+0 -9.79949E-3 -1.62575E-1 -3.10600E-1 -8.45988E-3 -1.34802E-1 -2.54002E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 5.04906E-5 1.82044E-3 1.09978E-2

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.80284E-7 -5.39678E-3 -3.84467E-2 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -2.72221E-5 -2.20842E-2 -1.61890E-1

K1 8.78991E-3(B1) 8.87834E-3(B1) 1.09005E-2(B1) 1.56982E-2(B1) 8.89226E-3(B1) 1.11165E-2(B1) 1.59861E-2(B1) K2 5.50807E-2(B2) 5.51978E-2(B2) 5.78707E-2(B2) 6.07794E-2(C1) 5.52001E-2(B2) 5.78922E-2(B2) 6.22687E-2(B2) K 3 8.77730E-2(C1) 8.77058E-2(C1) 7.34463E-2(C1) 6.60065E-2(B2) 8.77252E-2(C1) 7.71257E-2(C1) 6.94926E-2(C1) K4 1.54206E-1(B3) 1.54327E-1(B3) 1.56378E-1(B3) 1.63814E-1(B3) 1.54329E-1(B3) 1.56668E-1(B3) 1.64650E-1(B3) K 5 1.96149E-1(D1) 1.96265E-1(D1) 2.15896E-1(D1) 2.29610E-1(D1) 1.96237E-1(D1) 2.11010E-1(D1) 2.23781E-1(D1) K 6 3.02120E-1(B4) 3.02247E-1(B4) 3.04036E-1(B4) 3.10128E-1(B4) 3.02249E-1(B4) 3.04430E-1(B4) 3.11358E-1(B4) K 7 4.99295E-1(B5) 4.99425E-1(B5) 5.00883E-1(B5) 5.05419E-1(B5) 4.99427E-1(B5) 5.01361E-1(B5) 5.04379E-1(B5) K 8 5.45362E-1(C2) 5.45309E-1(C2) 5.35137E-1(C2) 5.21627E-1(C2) 5.45325E-1(C2) 5.38184E-1(C2) 5.31994E-1(C2)

表三十 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=10，

L

_T

a = 20

，

r = 1

，

α = 30

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.35038E-6 3.16077E-5 1.15967E-4 1.35715E-6 3.38428E-5 1.34325E-4 εb 0.00000E+0 -1.38710E-4 -2.47122E-3 -6.01926E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 1.42177E-5 3.79888E-4 1.56412E-3 1.99959E-5 4.98220E-4 1.97227E-3 Utip 0.00000E+0 -2.63103E-5 -6.25160E-3 -2.08933E-2 7.60623E-7 1.56177E-5 2.17180E-5 Vtip 0.00000E+0 -6.88577E-3 -1.05410E-1 -1.94290E-1 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 7.11665E-5 2.24679E-3 1.17842E-2 9.99794E-5 2.48719E-3 9.79756E-3

) 1

1(

Θ 0.00000E+0 3.11731E-7 -5.62620E-3 -3.83482E-2 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 -3.10413E-5 -2.31779E-2 -1.62919E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 8.78991E-3(B1) 8.90616E-3(B1) 1.13468E-2(B1) 1.64753E-2(B1) 8.93391E-3(B1) 1.18344E-2(B1) 1.78410E-2(B1) K2 5.50807E-2(B2) 5.52025E-2(B2) 5.79394E-2(B2) 6.35789E-2(B2) 5.52072E-2(B2) 5.80641E-2(B2) 6.51735E-2(B2) K 3 8.77730E-2(C1) 8.77443E-2(C1) 8.07937E-2(C1) 7.44041E-2(C1) 8.77818E-2(C1) 8.79942E-2(C1) 8.86576E-2(C1) K4 1.54206E-1(B3) 1.54330E-1(B3) 1.56904E-1(B3) 1.65165E-1(B3) 1.54334E-1(B3) 1.57220E-1(B3) 1.64118E-1(B3) K 5 1.96149E-1(D1) 1.96210E-1(D1) 2.06075E-1(D1) 2.16205E-1(D1) 1.96158E-1(D1) 1.96437E-1(D1) 1.98146E-1(D1) K 6 3.02120E-1(B4) 3.02251E-1(B4) 3.04773E-1(B4) 3.12299E-1(B4) 3.02254E-1(B4) 3.05326E-1(B4) 3.13488E-1(B4) K 7 4.99295E-1(B5) 4.99429E-1(B5) 5.01810E-1(B5) 5.06155E-1(B5) 4.99432E-1(B5) 5.02582E-1(B5) 5.10856E-1(B5) K 8 5.45362E-1(C2) 5.45342E-1(C2) 5.40926E-1(C2) 5.38618E-1(C2) 5.45374E-1(C2) 5.45658E-1(C2) 5.46543E-1(C2)

表三十一 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=10，

L

_T

a = 20

，

r = 1

，

α = 45

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.17216E-6 1.90826E-5 4.40434E-5 1.17915E-6 2.19883E-5 4.28298E-5 εb 0.00000E+0 -2.79653E-4 -5.53197E-3 -1.47105E-2 -2.41513E-4 -4.60030E-3 -1.17425E-2 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.42575E-5 3.91800E-4 1.55047E-3 Utip 0.00000E+0 -1.09694E-4 -3.23625E-2 -1.19806E-1 -8.15781E-5 -2.24609E-2 -8.57650E-2

Vtip 0.00000E+0 -1.39020E-2 -2.37527E-1 -4.52288E-1 -1.20018E-2 -1.98464E-1 -3.84874E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 7.14974E-5 3.26622E-3 2.50662E-2

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -1.33531E-5 -1.16956E-2 -8.45017E-2 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -8.00687E-5 -4.69958E-2 -3.52668E-1

K1 8.78991E-3(B1) 8.86478E-3(B1) 1.07708E-2(B1) 1.55854E-2(B1) 8.87857E-3(B1) 1.09162E-2(B1) 1.53785E-2(B1) K2 5.50807E-2(B2) 5.51848E-2(B2) 5.74785E-2(B2) 4.87412E-2(C1) 5.51873E-2(B2) 5.73844E-2(B2) 5.03044E-2(B2) K 3 8.77730E-2(C1) 8.76218E-2(C1) 6.35926E-2(C1) 6.52094E-2(B2) 8.76621E-2(C1) 6.86431E-2(C1) 6.69054E-2(C1) K4 1.54206E-1(B3) 1.54310E-1(B3) 1.55026E-1(B3) 1.59938E-1(B3) 1.54313E-1(B3) 1.55626E-1(B3) 1.61415E-1(B3) K 5 1.96149E-1(D1) 1.96377E-1(D1) 2.28178E-1(D1) 2.38675E-1(D1) 1.96321E-1(D1) 2.22140E-1(D1) 2.36187E-1(D1) K 6 3.02120E-1(B4) 3.02229E-1(B4) 3.02213E-1(B4) 3.03831E-1(B4) 3.02232E-1(B4) 3.03006E-1(B4) 3.06301E-1(B4) K 7 4.99295E-1(B5) 4.99405E-1(B5) 4.98617E-1(B5) 4.97250E-1(C2) 4.99408E-1(B5) 4.99445E-1(B5) 4.88142E-1B5) K 8 5.45362E-1(C2) 5.45241E-1(C2) 5.25397E-1(C2) 4.98955E-1(B5) 5.45274E-1(C2) 5.30870E-1(C2) 5.21437E-1(C2)

表三十二 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面a b=10，

L

_T

a = 20

，

r = 1

，

α = 45

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.18607E-6 2.47965E-5 6.02549E-5 1.19968E-6 2.98215E-5 1.17201E-4 εb 0.00000E+0 -1.96648E-4 -3.60768E-3 -8.77735E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 2.01072E-5 5.35142E-4 2.14609E-3 2.82791E-5 7.05037E-4 2.79612E-3 Utip 0.00000E+0 -5.38145E-5 -1.38116E-2 -5.26324E-2 6.75442E-7 1.00792E-5 -4.18425E-5

Vtip 0.00000E+0 -9.76877E-3 -1.56058E-1 -3.03584E-1 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 1.00733E-4 3.76203E-3 2.54285E-2 1.41397E-4 3.52028E-3 1.38996E-2

) 1

1(

Θ 0.00000E+0 -1.52111E-5 -1.23341E-2 -9.04580E-2 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 -9.16693E-5 -4.97593E-2 -3.77837E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 8.78991E-3(B1) 8.89235E-3(B1) 1.10969E-2(B1) 1.55017E-2(B1) 8.91986E-3(B1) 1.15360E-2(B1) 1.67982E-2(B1) K2 5.50807E-2(B2) 5.51897E-2(B2) 5.74487E-2(B2) 5.37005E-2(B2) 5.51945E-2(B2) 5.76679E-2(B2) 6.26660E-2(B2) K 3 8.77730E-2(C1) 8.77020E-2(C1) 7.42280E-2(C1) 6.91571E-2(C1) 8.77804E-2(C1) 8.79588E-2(C1) 8.85211E-2(C1) K4 1.54206E-1(B3) 1.54315E-1(B3) 1.56135E-1(B3) 1.62990E-1(B3) 1.54320E-1(B3) 1.56757E-1(B3) 1.60694E-1(B3) K 5 1.96149E-1(D1) 1.96266E-1(D1) 2.14867E-1(D1) 2.30712E-1(D1) 1.96157E-1(D1) 1.96480E-1(D1) 1.99011E-1(D1) K 6 3.02120E-1(B4) 3.02234E-1(B4) 3.03712E-1(B4) 3.08352E-1(B4) 3.02240E-1(B4) 3.04881E-1(B4) 3.10497E-1(B4) K 7 4.99295E-1(B5) 4.99411E-1(B5) 5.00364E-1(B5) 4.91636E-1(B5) 4.99418E-1(B5) 5.02108E-1(B5) 5.07536E-1(B5) K 8 5.45362E-1(C2) 5.45307E-1(C2) 5.35967E-1(C2) 5.32896E-1(C2) 5.45372E-1(C2) 5.45626E-1(C2) 5.46410E-1(C2)

表三十三 旋轉傾斜梁不同設定角不同轉速的振動頻率 (橢圓斷面

a b = 10

，L_T a=50，

r = 0

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99917E-5 1.24880E-3 4.98287E-3 4.99915E-5 1.24867E-3 4.98134E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 3.33327E-5 8.32918E-4 3.32673E-3 3.33326E-5 8.32844E-4 3.32582E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.38656E-3 3.34895E-2 1.19501E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.52770E-3 6.00833E-2 2.06372E-1

K1 3.51601E-3(B1) 5.04912E-3(B1) 1.04341E-2(B1) 1.46017E-2(B1) 7.00421E-3(B1) 1.92255E-2(B1) 2.67990E-2(B1) K2 2.20341E-2(B2) 3.21228E-2(B2) 6.44898E-2(C1) 1.12013E-1(C1) 3.25102E-2(B2) 6.24219E-2(C1) 1.09706E-1(C1) K 3 3.51520E-2(C1) 3.68086E-2(C1) 1.16218E-1(B2) 1.96337E-1(D1) 3.64868E-2(C1) 1.18966E-1(B2) 2.12822E-1(D1) K4 6.16949E-2(B3) 7.39788E-2(B3) 1.94766E-1(D1) 2.27180E-1(B2) 7.41481E-2(B3) 1.98212E-1(D1) 2.33180E-1(B2) K 5 1.20893E-1(B4) 1.34510E-1(B4) 2.04723E-1(B3) 3.36395E-1(C2) 1.34603E-1(B4) 2.06299E-1(B3) 3.31543E-1(D1) K 6 1.94214E-1(D1) 1.94234E-1(D1) 2.54232E-1(C2) 3.87453E-1(B3) 1.94361E-1(D1) 2.53000E-1(D1) 3.92529E-1(B3) K 7 1.99838E-1(B5) 2.14212E-1(B5) 3.06021E-1(B4) 5.57131E-1(B4) 2.14270E-1(B5) 3.07143E-1(B4) 5.59689E-1(B4) K 8 2.19989E-1(C2) 2.21462E-1(C2) 4.21041E-1(B5) 6.35978E-1(D2) 2.21404E-1(C2) 4.21824E-1(B5) 6.41061E-1(D2)

表三十四 旋轉傾斜梁不同設定角不同轉速的振動頻率 (橢圓斷面

a b = 10

，L_T a=50，

r = 0

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99914E-5 1.24864E-3 4.98116E-3 4.99917E-5 1.24880E-3 4.98287E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 3.33325E-5 8.32825E-4 3.32575E-3 3.33327E-5 8.32918E-4 3.32673E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 1.59893E-3 3.74511E-2 1.23522E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 2.91529E-3 6.74725E-2 2.16542E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 3.51601E-3(B1) 8.57346E-3(B1) 2.59141E-2(B1) 3.54931E-2(B1) 1.12025E-2(B1) 4.06850E-2(C1) 5.02236E-2(C1) K2 2.20341E-2(B2) 3.28927E-2(B2) 5.99460E-2(C1) 1.07179E-1(C1) 3.36436E-2(B2) 5.10812E-2(B1) 1.01077E-1(B1) K 3 3.51520E-2(C1) 3.61499E-2(C1) 1.21590E-1(B2) 2.24566E-1(D1) 3.54229E-2(C1) 1.26541E-1(B2) 2.41182E-1(D1) K4 6.16949E-2(B3) 7.43167E-2(B3) 2.01373E-1(D1) 2.38497E-1(B2) 7.46518E-2(B3) 2.07010E-1(D1) 2.48400E-1(B2) K 5 1.20893E-1(B4) 1.34696E-1(B4) 2.07819E-1(B3) 3.27706E-1(C2) 1.34881E-1(B4) 2.10758E-1(B3) 3.20819E-1(C1) K 6 1.94214E-1(D1) 1.94489E-1(D1) 2.51751E-1(C2) 3.95865E-1(B3) 1.94742E-1(D1) 2.49154E-1(C1) 4.00279E-1(B3) K 7 1.99838E-1(B5) 2.14329E-1(B5) 3.08187E-1(B4) 5.61985E-1(B4) 2.14445E-1(B5) 3.10092E-1(B4) 5.66135E-1(B4) K 8 2.19989E-1(C2) 2.21346E-1(C2) 4.22577E-1(B5) 6.45082E-1(D2) 2.21229E-1(C1) 4.24010E-1(B5) 6.51408E-1(D2)

表三十五 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面

a b = 10

，L_T a=50，

r = 1

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48966E-4 3.70759E-3 1.46317E-2 1.48965E-4 3.70749E-3 1.46309E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 8.33236E-5 2.07724E-3 8.23802E-3 8.33235E-5 2.07718E-3 8.23754E-3 V_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 W_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.38057E-3 3.03835E-2 8.91799E-2 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.51273E-3 5.27059E-2 1.40874E-1

K1 3.51601E-3(B1) 1.32574E-2(B1) 6.14098E-2(B1) 1.20715E-1(B1) 1.41186E-2(B1) 6.36059E-2(B1) 1.23005E-1(B1) K2 2.20341E-2(B2) 3.88823E-2(C1) 8.93752E-2(C1) 1.65717E-1(C1) 3.85776E-2(C1) 8.78209E-2(C1) 1.64024E-1(C1) K 3 3.51520E-2(C1) 4.32335E-2(B2) 1.81837E-1(B2) 2.33970E-1(D1) 4.35222E-2(B2) 1.83611E-1(B2) 2.46960E-1(D1) K4 6.16949E-2(B3) 8.86013E-2(B3) 2.05370E-1(D1) 3.58928E-1(B2) 8.87427E-2(B3) 2.08610E-1(D1) 3.62692E-1(B2) K 5 1.20893E-1(B4) 1.51857E-1(B4) 2.93304E-1(C2) 4.43232E-1(C2) 1.51939E-1(B4) 2.91939E-1(C2) 4.39984E-1(C2) K 6 1.94214E-1(D1) 1.94679E-1(D1) 3.03685E-1(B3) 5.86287E-1(B3) 1.94806E-1(D1) 3.05044E-1(B3) 5.89208E-1(B3) K 7 1.99838E-1(B5) 2.23407E-1(C2) 4.40838E-1(B4) 7.12545E-1(B4) 2.23349E-1(C2) 4.41598E-1(B4) 7.16774E-1(D2) K 8 2.19989E-1(C2) 2.33380E-1(B5) 5.93001E-1(B5) 8.27083E-1(B5) 2.33434E-1(B5) 5.93522E-1(B5) 8.28026E-1(B4)

表三十六 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面

a b = 10

，L_T a=50，

r = 1

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48965E-4 3.70747E-3 1.46308E-2 1.48966E-4 3.70759E-3 1.46317E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 8.33234E-5 2.07716E-3 8.23748E-3 8.33236E-5 2.07724E-3 8.23802E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 1.59205E-3 3.40811E-2 9.47869E-2 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 2.89813E-3 5.93556E-2 1.51650E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 3.51601E-3(B1) 1.49596E-2(B1) 6.60785E-2(B1) 1.25460E-1(B1) 1.66068E-2(B1) 7.39604E-2(C1) 1.31233E-1(C1) K2 2.20341E-2(B2) 3.82591E-2(C1) 8.59711E-2(C1) 1.62141E-1(C1) 3.75728E-2(C1) 7.92837E-2(B1) 1.57470E-1(B1) K 3 3.51520E-2(C1) 4.38087E-2(B2) 1.85328E-1(B2) 2.57153E-1(D1) 4.43753E-2(B2) 1.88627E-1(B2) 2.72673E-1(D1) K4 6.16949E-2(B3) 8.88836E-2(B3) 2.11607E-1(D1) 3.66192E-1(B2) 8.91641E-2(B3) 2.17001E-1(D1) 3.72920E-1(B2) K 5 1.20893E-1(B4) 1.52022E-1(B4) 2.90812E-1(C2) 4.37018E-1(C2) 1.52186E-1(B4) 2.88906E-1(C2) 4.31344E-1(C2) K 6 1.94214E-1(D1) 1.94933E-1(D1) 3.06119E-1(B3) 5.91496E-1(B3) 1.95186E-1(D1) 3.07801E-1(B3) 5.94963E-1(B3) K 7 1.99838E-1(B5) 2.23292E-1(C2) 4.42323E-1(B4) 7.20354E-1(D2) 2.23176E-1(C2) 4.43686E-1(B4) 7.26286E-1(D2) K 8 2.19989E-1(C2) 2.33488E-1(B5) 5.94050E-1(B5) 8.29439E-1(B4) 2.33595E-1(B5) 5.95122E-1(B5) 8.33265E-1(B4)

表三十七 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面

a b = 10

，L_T a=50，

r = 1

，

α = 30

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.28172E-6 2.45092E-5 9.51563E-5 1.30184E-6 1.97118E-5 -3.71419E-5 εb 0.00000E+0 -4.60802E-4 -5.23800E-3 -1.14857E-2 -3.93032E-4 -4.10599E-3 -8.03909E-3 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.61169E-5 7.25555E-4 2.41616E-3 Utip 0.00000E+0 -1.74189E-3 -6.82181E-2 -9.92978E-2 -1.26196E-3 -4.62429E-2 -7.71822E-2 Vtip 0.00000E+0 -5.53093E-2 -3.48918E-1 -4.25277E-1 -4.70926E-2 -2.87977E-1 -3.67897E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.41861E-4 1.96608E-2 7.14272E-2

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -4.96080E-4 -6.91289E-2 -2.21352E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -1.85739E-3 -2.70188E-1 -8.81548E-1

K1 3.51601E-3(B1) 3.73635E-3(B1) 7.37623E-3(B1) 1.32137E-2(B1) 3.76743E-3(B1) 7.43341E-3(B1) 1.26995E-2(B1) K2 2.20341E-2(B2) 2.23207E-2(B2) 2.35479E-2(C1) 2.80445E-2(C1) 2.23271E-2(B2) 2.42930E-2(B2) 2.52469E-2(B2) K 3 3.51520E-2(C1) 3.42313E-2(C1) 2.86687E-2(B2) 4.30789E-2(B2) 3.44837E-2(C1) 2.93646E-2(C1) 4.19193E-2(C1) K4 6.16949E-2(B3) 6.19598E-2(B3) 6.80978E-2(B3) 8.75335E-2(B3) 6.19738E-2(B3) 6.84189E-2(B3) 8.66233E-2(B3) K 5 1.20893E-1(B4) 1.21161E-1(B4) 1.26525E-1(B4) 1.48482E-1(B4) 1.21178E-1(B4) 1.26787E-1(B4) 1.45347E-1(B4) K 6 1.94214E-1(D1) 1.93115E-1(D1) 1.90042E-1(D1) 2.04763E-1(D1) 1.93430E-1(D1) 1.93185E-1(D1) 1.95992E-1(D1) K 7 1.99838E-1(B5) 2.00102E-1(B5) 2.04560E-1(B5) 2.13549E-1(C2) 2.00123E-1(B5) 2.07724E-1(B5) 2.17044E-1(B5) K 8 2.19989E-1(C2) 2.24459E-1(C2) 2.48453E-1(C2) 2.26737E-1(B5) 2.23242E-1(C2) 2.39933E-1(C2) 2.34668E-1(C2)

表三十八 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面

a b = 10

，L_T a=50，

r = 1

，

α = 30

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.32097E-6 2.18764E-5 -7.19948E-5 1.35641E-6 3.33988E-5 1.28155E-4 εb 0.00000E+0 -3.16137E-4 -3.03778E-3 -4.80546E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 3.63807E-5 9.75781E-4 3.33641E-3 4.99533E-5 1.22348E-3 4.60740E-3 Utip 0.00000E+0 -8.12945E-4 -2.70778E-2 -5.43232E-2 5.43647E-7 -1.11718E-4 -1.66579E-3

Vtip 0.00000E+0 -3.78117E-2 -2.20970E-1 -2.99895E-1 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 4.68535E-4 2.05650E-2 9.08061E-2 6.24203E-4 1.51392E-2 5.53003E-2

) 1

1(

Θ 0.00000E+0 -5.52042E-4 -7.08012E-2 -2.98952E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 -2.06978E-3 -2.78750E-1 -1.27047E+0 0.00000E+0 0.00000E+0 0.00000E+0

K1 3.51601E-3(B1) 3.79851E-3(B1) 7.63848E-3(B1) 1.22197E-2(B1) 3.86062E-3(B1) 8.40076E-3(B1) 1.26341E-2(B1) K2 2.20341E-2(B2) 2.23336E-2(B2) 2.55641E-2(B2) 2.30000E-2(B2) 2.23464E-2(B2) 2.77333E-2(B2) 2.89172E-2(C1) K 3 3.51520E-2(C1) 3.47248E-2(C1) 3.03690E-2(C1) 4.12725E-2(C1) 3.51741E-2(C1) 3.57047E-2(C1) 3.73553E-2(B2) K4 6.16949E-2(B3) 6.19870E-2(B3) 6.85597E-2B3) 8.65717E-2(B3) 6.20111E-2(B3) 6.77171E-2(B3) 6.93085E-2(B3) K 5 1.20893E-1(B4) 1.21194E-1(B4) 1.27179E-1(B4) 1.42881E-1(B4) 1.21224E-1(B4) 1.27316E-1B4) 1.29765E-1(B4) K 6 1.94214E-1(D1) 1.93719E-1(D1) 1.97393E-1(D1) 1.90181E-1(D1) 1.94222E-1(D1) 1.94163E-1(D1) 1.93076E-1(D1) K 7 1.99838E-1(B5) 2.00142E-1(B5) 2.09012E-1(B5) 2.20600E-1(B5) 2.00178E-1(B5) 2.06819E-1(B5) 2.12857E-1(B5) K 8 2.19989E-1(C2) 2.22097E-1(C2) 2.29663E-1(C2) 2.40566E-1(C2) 2.20018E-1(C2) 2.20720E-1(C2) 2.22858E-1(C2)

表三十九 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面

a b = 10

，L_T a=50，

r = 1

，

α = 45

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.04479E-6 9.32842E-6 3.03888E-5 1.08557E-6 -1.82846E-5 -3.87333E-4 εb 0.00000E+0 -6.60054E-4 -7.73609E-3 -1.69917E-2 -5.63024E-4 -6.02066E-3 -1.18004E-2 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.69269E-5 9.39054E-4 2.57646E-3 Utip 0.00000E+0 -3.60131E-3 -1.50528E-1 -2.18568E-1 -2.61180E-3 -1.14322E-1 -1.99322E-1

Vtip 0.00000E+0 -7.94603E-2 -5.05783E-1 -6.09499E-1 -6.76969E-2 -4.41048E-1 -5.57751E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 5.04325E-4 4.75797E-2 1.56612E-1

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -1.02476E-3 -1.48447E-1 -4.08634E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -3.80937E-3 -5.84689E-1 -1.69078E+0

K1 3.51601E-3(B1) 3.70954E-3(B1) 7.33126E-3(B1) 1.31589E-2(B1) 3.73853E-3(B1) 7.07299E-3(B1) 1.23238E-2(B1) K2 2.20341E-2(B2) 2.22835E-2(B2) 1.88374E-2(C1) 2.40428E-2(C1) 2.22909E-2(B2) 1.85715E-2(B2) 2.09105E-2(B2) K 3 3.51520E-2(C1) 3.32889E-2(C1) 2.83444E-2(B2) 4.28804E-2(B2) 3.37749E-2(C1) 2.87893E-2(C1) 4.17330E-2(C1) K4 6.16949E-2(B3) 6.18787E-2(B3) 6.63327E-2(B3) 8.61240E-2(B3) 6.19056E-2(B3) 6.69048E-2(B3) 8.56783E-2(B3) K 5 1.20893E-1(B4) 1.21062E-1(B4) 1.23355E-1(B4) 1.44251E-1(B4) 1.21096E-1(B4) 1.22807E-1(B4) 1.35704E-1(B4) K 6 1.94214E-1(D1) 1.91979E-1(D1) 1.72119E-1(D1) 1.93201E-1(D1) 1.92593E-1(D1) 1.73672E-1(D1) 1.76233E-1(D1) K 7 1.99838E-1(B5) 1.99989E-1(B5) 2.00390E-1(B5) 2.19417E-1(B5) 2.00029E-1(B5) 2.05312E-1(B5) 2.31054E-1(B5) K 8 2.19989E-1(C2) 2.28930E-1(C2) 2.72263E-1(C2) 2.23423E-1(C2) 2.26564E-1(C2) 2.70310E-1(C2) 2.40421E-1(C2)

表四十 旋轉傾斜梁不同設定角不同轉速的振動頻率(橢圓斷面

a b = 10

，L_T a=50，

r = 1

，

α = 45

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.12472E-6 -2.02031E-5 -5.84272E-4 1.19819E-6 2.89254E-5 1.04471E-4 εb 0.00000E+0 -4.52884E-4 -4.31500E-3 -6.70674E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 5.14477E-5 1.31461E-3 3.57148E-3 7.06559E-5 1.73678E-3 6.59985E-3 Utip 0.00000E+0 -1.68416E-3 -7.42735E-2 -1.75671E-1 2.41305E-7 -2.47147E-4 -3.53304E-3

V_tip 0.00000E+0 -5.43835E-2 -3.56719E-1 -4.86204E-1 0.00000E+0 0.00000E+0 0.00000E+0 W_tip 0.00000E+0 6.81377E-4 5.06232E-2 2.32526E-1 8.82937E-4 2.15128E-2 7.94496E-2

) 1

1(

Θ 0.00000E+0 -1.14160E-3 -1.72348E-1 -6.27280E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 -4.24807E-3 -6.79913E-1 -2.70566E+0 0.00000E+0 0.00000E+0 0.00000E+0

K1 3.51601E-3(B1) 3.76780E-3(B1) 6.96556E-3(B1) 1.16619E-2(B1) 3.82705E-3(B1) 7.69318E-3(B1) ****

K2 2.20341E-2(B2) 2.22982E-2(B2) 1.90931E-2(B2) 1.90486E-2(B2) 2.23132E-2(B2) 2.58104E-2(B2) 1.32059E-2(B2) K 3 3.51520E-2(C1) 3.42509E-2(C1) 2.93213E-2(C1) 4.14259E-2(C1) 3.51705E-2(C1) 3.56220E-2(C1) 3.46933E-2(C1) K4 6.16949E-2(B3) 6.19308E-2(B3) 6.76296E-2(B3) 8.60007E-2(B3) 6.19764E-2(B3) 6.54145E-2(B3) 3.70871E-2(B3) K 5 1.20893E-1(B4) 1.21128E-1(B4) 1.23336E-1(B4) 1.22754E-1(B4) 1.21187E-1(B4) 1.24832E-1(B4) 9.72304E-2(B4) K 6 1.94214E-1(D1) 1.93172E-1(D1) 1.78450E-1(D1) 1.69124E-1(D1) 1.94220E-1(D1) 1.93755E-1(D1) 1.75639E-1(D1) K 7 1.99838E-1(B5) 2.00068E-1(B5) 2.09558E-1(B5) 2.39371E-1(B5) 2.00141E-1(B5) 2.04636E-1(B5) 1.98523E-1(B5) K 8 2.19989E-1(C2) 2.24287E-1(C2) 2.62081E-1(C2) 2.58753E-1(C2) 2.20015E-1(C2) 2.20637E-1(C2) 2.22485E-1(C2)

表四十一 旋轉傾斜梁不同設定角不同轉速的振動頻率 (I 型斷面

W 10 × 30

，

L

_T

d

_nom

= 25

，

r = 0

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99917E-5 1.24880E-3 4.98287E-3 4.99910E-5 1.24850E-3 4.98081E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 3.33327E-5 8.32918E-4 3.32673E-3 3.33133E-5 8.26850E-4 3.30372E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.00157E-2 1.79396E-1 3.54795E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 9.70138E-3 1.84407E-1 4.11350E-1

K1 1.94103E-2(B1) 1.98919E-2(B1) 2.68274E-2(B1) 3.55766E-2(B1) 2.05015E-2(B1) 3.37227E-2(B1) 4.56895E-2(B1) K2 6.15796E-2(C1) 6.25198E-2(C1) 7.24914E-2(C1) 8.42532E-2(C1) 6.23275E-2(C1) 7.90719E-2(C1) 1.20153E-1(C1) K 3 6.79899E-2(D1) 6.82173E-2(D1) 8.24975E-2(D1) 1.24550E-1(D1) 6.85190E-2(D1) 8.34524E-2(D1) 1.26470E-1(D1) K4 1.21591E-1(B2) 1.23823E-1(B2) 1.68670E-1(B2) 2.62135E-1(B2) 1.23929E-1(B2) 1.71637E-1(B2) 2.70949E-1(B2) K 5 2.33196E-1(D2) 2.34498E-1(D2) 2.63488E-1(D2) 3.36180E-1(D2) 2.34588E-1(D2) 2.66437E-1(D2) 3.48155E-1(D2) K 6 3.40225E-1(B3) 3.42693E-1(B3) 3.96841E-1(B3) 4.61393E-1(C2) 3.42704E-1(B3) 3.82485E-1(B3) 4.44601E-1(C2) K 7 3.84279E-1(C2) 3.85125E-1(C2) 4.04913E-1(C2) 5.28116E-1(B3) 3.85119E-1C2) 4.20170E-1(C2) 5.47516E-1(B3) K 8 4.80846E-1(D3) 4.82686E-1(D3) 5.24537E-1(D3) 6.34876E-1(D3) 4.82730E-1(D3) 5.26141E-1(D3) 6.41514E-1(D3)

表四十二 旋轉傾斜梁不同設定角不同轉速的振動頻率 (I 型斷面W10×30，

L

_T

d

_nom

= 25

，

r = 0

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99908E-5 1.24849E-3 4.98107E-3 4.99917E-5 1.24880E-3 4.98287E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 3.33073E-5 8.26924E-4 3.30855E-3 3.33327E-5 8.32918E-4 3.32673E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 1.14614E-2 1.77821E-1 3.13634E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 1.11171E-2 1.87596E-1 3.82199E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.94103E-2(B1) 2.10993E-2(B1) 4.01032E-2(B1) 5.45816E-2(B1) 2.22648E-2(B1) 5.67613E-2(B1) 7.33371E-2(C1) K2 6.15796E-2(C1) 6.21323E-2(C1) 7.63679E-2(C1) 1.16926E-1(C1) 6.17335E-2(C1) 6.51434E-2(C1) 1.06222E-1(B1) K 3 6.79899E-2(D1) 6.88143E-2(D1) 8.92494E-2(D1) 1.39356E-1(D1) 6.93863E-2(D1) 9.69279E-2(D1) 1.53395E-1(D1) K4 1.21591E-1(B2) 1.24031E-1(B2) 1.73506E-1(B2) 2.75157E-1(B2) 1.24227E-1(B2) 1.75957E-1(B2) 2.80770E-1(B2) K 5 2.33196E-1(D2) 2.34677E-1(D2) 2.68414E-1(D2) 3.53404E-1(D2) 2.34849E-1(D2) 2.71191E-1(D2) 3.59919E-1(D2) K 6 3.40225E-1(B3) 3.42733E-1(B3) 3.82637E-1(B3) 4.44374E-1(B3) 3.42839E-1(B3) 4.00005E-1(B3) 4.49676E-1(C2) K 7 3.84279E-1(C2) 3.85094E-1(C2) 4.19966E-1(C2) 5.46471E-1(C2) 3.84989E-1(C2) 4.01638E-1(C2) 5.37660E-1(B3) K 8 4.80846E-1(D3) 4.82773E-1(D3) 5.27130E-1(D3) 6.44261E-1(D3) 4.82855E-1(D3) 5.28414E-1(D3) 6.47635E-1(D3)

表四十三 旋轉傾斜梁不同設定角不同轉速的振動頻率 (I 型斷面W10×30，

L

_T

d

_nom

= 25

，r =1，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48966E-4 3.70759E-3 1.46316E-2 1.48965E-4 3.70744E-3 1.46310E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 8.33235E-5 2.07724E-3 8.23801E-3 8.33055E-5 2.07481E-3 8.23244E-3 V_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 W_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 9.69277E-3 1.15457E-1 1.79688E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 9.40173E-3 1.19860E-1 2.01016E-1

K1 1.94103E-2(B1) 2.34955E-2(B1) 6.68272E-2(B1) 1.25630E-1(B1) 2.40137E-2(B1) 6.98552E-2(B1) 1.29014E-1(B1) K2 6.15796E-2(C1) 6.37650E-2(C1) 9.55046E-2(C1) 1.48282E-1(C1) 6.35769E-2(C1) 1.00386E-1(C1) 1.67521E-1(C1) K 3 6.79899E-2(D1) 6.93852E-2(D1) 1.03537E-1(D1) 1.75422E-1(D1) 6.96814E-2(D1) 1.03541E-1(D1) 1.73532E-1(D1) K4 1.21591E-1(B2) 1.27265E-1(B2) 2.22348E-1(B2) 3.86444E-1(B2) 1.27367E-1(B2) 2.24190E-1(B2) 3.90847E-1(B2) K 5 2.33196E-1(D2) 2.36522E-1(D2) 3.03660E-1(D2) 4.44960E-1(D2) 2.36611E-1(D2) 3.05873E-1(D2) 4.51728E-1(D2) K 6 3.40225E-1(B3) 3.46309E-1(B3) 4.30745E-1(C2) 5.45943E-1(C2) 3.46320E-1(B3) 4.26701E-1(C2) 5.41397E-1(C2) K 7 3.84279E-1(C2) 3.86250E-1(C2) 4.66072E-1(B3) 7.07933E-1(B3) 3.86243E-1(C2) 4.70367E-1(B3) 7.12476E-1(B3) K 8 4.80846E-1(D3) 4.85374E-1(D3) 5.81227E-1(D3) 7.97206E-1(D3) 4.85418E-1(D3) 5.82416E-1(D3) 8.00975E-1(D3)

表四十四 旋轉傾斜梁不同設定角不同轉速的振動頻率 (I 型斷面W10×30，

L

_T

d

_nom

= 25

，r =1，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48965E-4 3.70742E-3 1.46309E-2 1.48966E-4 3.70759E-3 1.46316E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 8.32999E-5 2.07458E-3 8.23249E-3 8.33235E-5 2.07724E-3 8.23801E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 1.10953E-2 1.20539E-1 1.78426E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 1.07767E-2 1.27649E-1 2.06474E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.94103E-2(B1) 2.45261E-2(B1) 7.31816E-2(B1) 1.32720E-1(B1) 2.55361E-2(B1) 8.35606E-2(B1) 1.42645E-1(C1) K2 6.15796E-2(C1) 6.33858E-2(C1) 9.85971E-2(C1) 1.69410E-1(C1) 6.29948E-2(C1) 9.00878E-2(C1) 1.61312E-1(B1) K 3 6.79899E-2(D1) 6.99715E-2(D1) 1.08036E-1(D1) 1.80889E-1(D1) 7.05343E-2(D1) 1.15282E-1(D1) 1.96214E-1(D1) K4 1.21591E-1(B2) 1.27467E-1(B2) 2.25653E-1(B2) 3.94195E-1(B2) 1.27658E-1(B2) 2.27950E-1(B2) 3.99522E-1(B2) K 5 2.33196E-1(D2) 2.36699E-1(D2) 3.07629E-1(D2) 4.56440E-1(D2) 2.36870E-1(D2) 3.10378E-1(D2) 4.63255E-1(D2) K 6 3.40225E-1(B3) 3.46348E-1(B3) 4.25732E-1(C2) 5.38838E-1(C2) 3.46454E-1(B3) 4.27646E-1(C2) 5.35831E-1(C2) K 7 3.84279E-1(C2) 3.86218E-1(C2) 4.71268E-1(B3) 7.14315E-1(B3) 3.86113E-1(C2) 4.68782E-1(B3) 7.15203E-1(B3) K 8 4.80846E-1(D3) 4.85460E-1(D3) 5.83333E-1(D3) 8.03600E-1(D3) 4.85542E-1(D3) 5.84732E-1(D3) 8.07426E-1(D3)

表四十五 旋轉傾斜梁不同設定角不同轉速的振動頻率 (I 型斷面

W 10 × 30

，

L

_T

d

_nom

= 25

，

r = 1

，

α = 30

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.35440E-6 3.23381E-5 1.17467E-4 1.35505E-6 3.27038E-5 1.20428E-4 εb 0.00000E+0 -9.50303E-5 -2.22663E-3 -7.53389E-3 -8.22550E-5 -1.90605E-3 -6.29422E-3 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 8.53165E-6 2.18437E-4 8.80206E-4 Utip 0.00000E+0 -1.61612E-6 -1.20445E-3 -1.14604E-2 -1.02425E-6 -8.84581E-4 -8.69421E-3

Vtip 0.00000E+0 -2.04194E-3 -4.63348E-2 -1.42525E-1 -1.76730E-3 -3.97202E-2 -1.22857E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.01857E-4 2.79323E-3 1.67988E-2

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 7.19711E-5 -1.39029E-2 -1.64752E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.39133E-5 -3.35855E-2 -3.88867E-1

K1 1.94103E-2(B1) 1.94503E-2(B1) 2.04094E-2(B1) 2.32806E-2(B1) 1.94567E-2(B1) 2.05186E-2(B1) 2.32611E-2(B1) K2 6.15796E-2(C1) 6.15765E-2(C1) 5.63103E-2(C1) 4.63547E-2(C1) 6.15805E-2(C1) 5.72816E-2(C1) 4.68945E-2(C1) K 3 6.79899E-2(D1) 6.80266E-2(D1) 7.43309E-2(D1) 8.79299E-2(D1) 6.80233E-2(D1) 7.32198E-2(D1) 8.64024E-2(D1) K4 1.21591E-1(B2) 1.21644E-1(B2) 1.22894E-1(B2) 1.26660E-1(B2) 1.21645E-1(B2) 1.22961E-1(B2) 1.28009E-1(B2) K 5 2.33196E-1(D2) 2.33234E-1(D2) 2.37282E-1(D2) 2.58652E-1(D2) 2.33233E-1(D2) 2.36392E-1(D2) 2.54728E-1(D2) K 6 3.40225E-1(B3) 3.40281E-1(B3) 3.41449E-1(B3) 3.44188E-1(B3) 3.40281E-1(B3) 3.41438E-1(B3) 3.38967E-1(B3) K 7 3.84279E-1(C2) 3.84299E-1(C2) 3.85704E-1(C2) 3.95076E-1(C2) 3.84299E-1(C2) 3.85495E-1(C2) 3.99172E-1(C2) K 8 4.80846E-1(D3) 4.80893E-1(D3) 4.84055E-1(D3) 5.04670E-1(D3) 4.80892E-1(D3) 4.83478E-1(D3) 5.00062E-1(D3)

表四十六 旋轉傾斜梁不同設定角不同轉速的振動頻率 (I 型斷面

W 10 × 30

，

L

_T

d

_nom

= 25

，

r = 1

，

α = 30

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.35571E-6 3.30617E-5 1.23961E-4 1.35701E-6 3.37528E-5 1.32971E-4 εb 0.00000E+0 -6.71253E-5 -1.53836E-3 -4.94065E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 1.20592E-5 3.05616E-4 1.22215E-3 1.70362E-5 4.23028E-4 1.65735E-3 Utip 0.00000E+0 -4.33832E-7 -5.76513E-4 -5.88731E-3 7.42689E-7 4.66992E-6 -1.41152E-4

Vtip 0.00000E+0 -1.44212E-3 -3.20994E-2 -9.98665E-2 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 1.43969E-4 3.81434E-3 2.08090E-2 2.03379E-4 5.03405E-3 1.95266E-2

) 1

1(

Θ 0.00000E+0 8.31436E-5 -1.56721E-2 -1.97144E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 3.92487E-5 -3.79728E-2 -4.58869E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.94103E-2(B1) 1.94630E-2(B1) 2.06325E-2(B1) 2.32776E-2(B1) 1.94757E-2(B1) 2.08744E-2(B1) 2.35508E-2(B1) K2 6.15796E-2(C1) 6.15844E-2(C1) 5.84212E-2(C1) 4.81392E-2(C1) 6.15922E-2(C1) 6.18950E-2(C1) 6.28410E-2(C1) K 3 6.79899E-2(D1) 6.80201E-2(D1) 7.19431E-2(D1) 8.39745E-2(D1) 6.80136E-2(D1) 6.82043E-2(D1) 6.50950E-2(D1) K4 1.21591E-1(B2) 1.21646E-1(B2) 1.23021E-1(B2) 1.28895E-1(B2) 1.21648E-1(B2) 1.23122E-1(B2) 1.28393E-1(B2) K 5 2.33196E-1(D2) 2.33232E-1(D2) 2.35515E-1(D2) 2.49587E-1(D2) 2.33230E-1(D2) 2.33804E-1(D2) 2.33015E-1(D2) K 6 3.40225E-1(B3) 3.40282E-1(B3) 3.41468E-1(B3) 3.36383E-1(B3) 3.40283E-1(B3) 3.41640E-1(B3) 3.45442E-1(B3) K 7 3.84279E-1(C2) 3.84298E-1(C2) 3.85255E-1(C2) 3.99934E-1(C2) 3.84296E-1(C2) 3.84700E-1(C2) 3.85948E-1(C2) K 8 4.80846E-1(D3) 4.80891E-1(D3) 4.82922E-1(D3) 4.95076E-1(D3) 4.80890E-1(D3) 4.81868E-1(D3) 4.84189E-1(D3)

表四十七 旋轉傾斜梁不同設定角不同轉速的振動頻率 (I 型斷面

W 10 × 30

，

L

_T

d

_nom

= 25

，

r = 1

，

α = 45

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.19416E-6 2.67401E-5 8.13308E-5 1.19547E-6 2.74613E-5 8.48984E-5 εb 0.00000E+0 -1.34463E-4 -3.18341E-3 -1.09552E-2 -1.16386E-4 -2.72501E-3 -9.15539E-3 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.20662E-5 3.08698E-4 1.21097E-3 Utip 0.00000E+0 -4.08446E-6 -2.49978E-3 -2.46805E-2 -2.89916E-6 -1.85578E-3 -1.98795E-2

Vtip 0.00000E+0 -2.88966E-3 -6.64191E-2 -2.07868E-1 -2.50102E-3 -5.71237E-2 -1.83002E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.44080E-4 4.24859E-3 3.28457E-2

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 4.23293E-5 -3.06142E-2 -3.12277E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -3.04093E-5 -7.03074E-2 -7.42180E-1

K1 1.94103E-2(B1) 1.94439E-2(B1) 2.02820E-2(B1) 2.30059E-2(B1) 1.94502E-2(B1) 2.03514E-2(B1) 2.27930E-2(B1) K2 6.15796E-2(C1) 6.15510E-2(C1) 5.31033E-2(C1) 4.08746E-2(C1) 6.15608E-2(C1) 5.43504E-2(C1) 4.04931E-2(C1) K 3 6.79899E-2(D1) 6.80488E-2(D1) 7.76661E-2(D1) 9.38004E-2(D1) 6.80394E-2(D1) 7.61490E-2(D1) 9.30702E-2(D1) K4 1.21591E-1(B2) 1.21638E-1(B2) 1.22730E-1(B2) 1.25936E-1(B2) 1.21639E-1(B2) 1.22858E-1(B2) 1.29243E-1(B2) K 5 2.33196E-1(D2) 2.33237E-1(D2) 2.40481E-1(D2) 2.70380E-1(D2) 2.33235E-1(D2) 2.38803E-1(D2) 2.66228E-1(D2) K 6 3.40225E-1(B3) 3.40275E-1(B3) 3.41108E-1(B3) 3.41766E-1(B3) 3.40275E-1(B3) 3.40921E-1(B3) 3.33581E-1(B3) K 7 3.84279E-1(C2) 3.84300E-1(C2) 3.86790E-1(C2) 4.09048E-1(C2) 3.84298E-1(C2) 3.86510E-1(C2) 4.19303E-1(C2) K 8 4.80846E-1(D3) 4.80893E-1(D3) 4.86222E-1(D3) 5.26110E-1(D3) 4.80891E-1(D3) 4.85060E-1(D3) 5.19582E-1(D3)

表四十八 旋轉傾斜梁不同設定角不同轉速的振動頻率 (I 型斷面

W 10 × 30

，

L

_T

d

_nom

= 25

，

r = 1

，

α = 45

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.19678E-6 2.81864E-5 9.03004E-5 1.19939E-6 2.96407E-5 1.14452E-4 εb 0.00000E+0 -9.49787E-5 -2.19896E-3 -7.15255E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 1.70551E-5 4.32248E-4 1.69665E-3 2.40940E-5 5.99016E-4 2.35520E-3 Utip 0.00000E+0 -1.71673E-6 -1.22599E-3 -1.46244E-2 6.39568E-7 -1.19008E-5 -3.72364E-4

Vtip 0.00000E+0 -2.04085E-3 -4.63098E-2 -1.53295E-1 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 2.03638E-4 5.67995E-3 4.14226E-2 2.87641E-4 7.13085E-3 2.77844E-2

) 1

1(

Θ 0.00000E+0 4.89641E-5 -3.50172E-2 -4.10827E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 -3.49292E-5 -8.03456E-2 -9.47913E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.94103E-2(B1) 1.94565E-2(B1) 2.04280E-2(B1) 2.25019E-2(B1) 1.94691E-2(B1) 2.06045E-2(B1) 2.04634E-2(B1) K2 6.15796E-2(C1) 6.15706E-2(C1) 5.59159E-2(C1) 4.04958E-2(C1) 6.15902E-2(C1) 6.18454E-2(C1) 5.93081E-2(D1) K 3 6.79899E-2(D1) 6.80299E-2(D1) 7.43005E-2(D1) 9.18500E-2(D1) 6.80111E-2(D1) 6.77603E-2(D1) 6.26558E-2(C1) K4 1.21591E-1(B2) 1.21640E-1(B2) 1.22960E-1(B2) 1.32058E-1(B2) 1.21643E-1(B2) 1.23087E-1(B2) 1.28953E-1(B2) K 5 2.33196E-1(D2) 2.33232E-1(D2) 2.37073E-1(D2) 2.61793E-1(D2) 2.33226E-1(D2) 2.33471E-1(D2) 2.28934E-1(D2) K 6 3.40225E-1(B3) 3.40276E-1(B3) 3.40916E-1(B3) 3.26352E-1(B3) 3.40277E-1(B3) 3.41462E-1(B3) 3.44319E-1(B3) K 7 3.84279E-1(C2) 3.84297E-1(C2) 3.86062E-1(C2) 4.25021E-1(C2) 3.84294E-1(C2) 3.84654E-1(C2) 3.85754E-1(C2) K 8 4.80846E-1(D3) 4.80889E-1(D3) 4.83917E-1(D3) 5.11068E-1(D3) 4.80886E-1(D3) 4.81694E-1(D3) 4.82723E-1(D3)

表四十九 旋轉傾斜梁不同設定角不同轉速的振動頻率 (十字斷面

d × b × t = 14 × 7 × 0 . 35

，

L

_T

d = 20

，

r = 0

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99917E-5 1.24880E-3 4.98287E-3 4.99717E-5 1.24339E-3 4.96404E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 3.33327E-5 8.32918E-4 3.32673E-3 3.33154E-5 8.28797E-4 3.31449E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.28247E-2 2.06304E-1 3.68389E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.33695E-2 3.37062E-1 5.51809E-1

K1 1.48090E-2(B1) 1.54271E-2(B1) 2.27288E-2(B1) 3.07058E-2(B1) 1.61904E-2(B1) 2.85269E-2(B1) 3.81977E-2(B1) K2 4.17796E-2(C1) 4.31793E-2(C1) 6.20044E-2(C1) 7.55019E-2(C1) 4.28984E-2(C1) 6.60944E-2(C1) 1.12277E-1(C1) K 3 5.63311E-2(D1) 5.66008E-2(D1) 6.86566E-2(D1) 1.14928E-1(D1) 5.69569E-2(D1) 7.44531E-2(D1) 1.19951E-1(D1) K4 9.27837E-2(B2) 9.56912E-2(B2) 1.49101E-1(B2) 2.49147E-1(B2) 9.58285E-2(B2) 1.52431E-1(B2) 2.57833E-1(B2) K 5 1.69162E-1(D2) 1.71175E-1(D2) 2.11616E-1(D2) 2.97648E-1(D2) 1.71296E-1(D2) 2.15781E-1(D2) 3.11672E-1(D2) K 6 2.59694E-1(B3) 2.62556E-1(C2) 2.90763E-1(C2) 3.65107E-1(C2) 2.61788E-1(B3) 2.85154E-1(C2) 3.55694E-1(C2) K 7 2.61316E-1(C2) 2.62918E-1(B3) 3.30025E-1(B3) 4.77649E-1(B3) 2.63688E-1(C2) 3.36158E-1(B3) 4.88217E-1(B3) K 8 2.82499E-1(D2) 2.86011E-1(D2) 3.55995E-1(D2) 5.02328E-1(D2) 2.86087E-1(D2) 3.59124E-1(D2) 5.11889E-1(D2)

表五十 旋轉傾斜梁不同設定角不同轉速的振動頻率 (十字斷面

d × b × t = 14 × 7 × 0 . 35

，

L

_T

d = 20

，

r = 0

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 4.99655E-5 1.24338E-3 4.96662E-3 4.99917E-5 1.24880E-3 4.98287E-3 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 3.33102E-5 8.29035E-4 3.31721E-3 3.33327E-5 8.32918E-4 3.32673E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 1.46273E-2 1.98940E-1 3.21494E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 2.66975E-2 3.33725E-1 5.03722E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.48090E-2(B1) 1.69352E-2(B1) 3.37336E-2(B1) 4.44769E-2(B1) 1.83851E-2(B1) 4.66801E-2(C1) 5.60331E-2(C1) K2 4.17796E-2(C1) 4.26101E-2(C1) 6.36524E-2(C1) 1.10082E-1(C1) 4.20076E-2(C1) 5.49385E-2(B1) 1.04672E-1(B1) K 3 5.63311E-2(D1) 5.73004E-2(D1) 8.06928E-2(D1) 1.32644E-1(D1) 5.79527E-2(D1) 8.80579E-2(D1) 1.45795E-1(D1) K4 9.27837E-2(B2) 9.59610E-2(B2) 1.54488E-1(B2) 2.62236E-1(B2) 9.62130E-2(B2) 1.57290E-1(B2) 2.68665E-1(B2) K 5 1.69162E-1(D2) 1.71413E-1(D2) 2.18029E-1(D2) 3.16901E-1(D2) 1.71630E-1(D2) 2.20655E-1(D2) 3.22920E-1(D2) K 6 2.59694E-1(B3) 2.61650E-1(B3) 2.84394E-1(C2) 3.53145E-1(C2) 2.62361E-1(C2) 2.86290E-1(C2) 3.50528E-1(C2) K 7 2.61316E-1(C2) 2.63826E-1(C2) 3.36681E-1(B3) 4.89229E-1(B3) 2.63108E-1(B3) 3.33809E-1(B3) 4.88145E-1(B3) K 8 2.82499E-1(D2) 2.86158E-1(D2) 3.60430E-1(D2) 5.14774E-1(D2) 2.86282E-1(D2) 3.61421E-1(D2) 5.17618E-1(D2)

表五十一 旋轉傾斜梁不同設定角不同轉速的振動頻率 (十字斷面

d × b × t = 14 × 7 × 0 . 35

，

L

_T

d = 20

，

r = 1

，

α = 0

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48966E-4 3.70759E-3 1.46316E-2 1.48948E-4 3.70598E-3 1.46285E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 U_tip 0.00000E+0 8.33235E-5 2.07724E-3 8.23801E-3 8.33081E-5 2.07590E-3 8.23541E-3 V_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 W_tip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 1.22145E-2 1.22014E-1 1.77771E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.18572E-2 1.72179E-1 2.21635E-1

K1 1.48090E-2(B1) 1.98458E-2(B1) 6.50967E-2(B1) 1.24134E-1(B1) 2.04444E-2(B1) 6.73118E-2(B1) 1.26303E-1(B1) K2 4.17796E-2(C1) 4.49612E-2(C1) 8.80689E-2(C1) 1.43382E-1(C1) 4.46920E-2(C1) 9.06198E-2(C1) 1.62585E-1(C1) K 3 5.63311E-2(D1) 5.80943E-2(D1) 9.26771E-2(D1) 1.68046E-1(D1) 5.84404E-2(D1) 9.58419E-2(D1) 1.66803E-1(D1) K4 9.27837E-2(B2) 1.00100E-1(B2) 2.07242E-1(B2) 3.76404E-1(B2) 1.00231E-1(B2) 2.09173E-1(B2) 3.80647E-1(B2) K 5 1.69162E-1(D2) 1.74450E-1(D2) 2.61907E-1(D2) 4.15747E-1(D2) 1.74569E-1(D2) 2.64495E-1(D2) 4.22780E-1(D2) K 6 2.59694E-1(B3) 2.64200E-1(C2) 3.25606E-1(C2) 4.66197E-1(C2) 2.63944E-1(C2) 3.23729E-1(C2) 4.62262E-1(C2) K 7 2.61316E-1(C2) 2.67607E-1(B3) 4.09116E-1(B3) 6.65943E-1(B3) 2.67864E-1(B3) 4.10986E-1(B3) 6.69497E-1(B3) K 8 2.82499E-1(D2) 2.91298E-1(D2) 4.35603E-1(D2) 6.85468E-1(D2) 2.91373E-1(D2) 4.37311E-1(D2) 6.89931E-1(D2)

表五十二 旋轉傾斜梁不同設定角不同轉速的振動頻率 (十字斷面

d × b × t = 14 × 7 × 0 . 35

，

L

_T

d = 20

，

r = 1

，

α = 0

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-2 5.00000E-2 1.00000E-1 1.00000E-2 5.00000E-2 1.00000E-1

ε0 0.00000E+0 1.48942E-4 3.70577E-3 1.46283E-2 1.48966E-4 3.70759E-3 1.46316E-2 εb 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Utip 0.00000E+0 8.33034E-5 2.07580E-3 8.23544E-3 8.33235E-5 2.07724E-3 8.23801E-3 Vtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0

) 1

1(

Θ 0.00000E+0 1.39400E-2 1.26208E-1 1.76257E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 2.49843E-2 1.81618E-1 2.26716E-1 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.48090E-2(B1) 2.10390E-2(B1) 6.97541E-2(B1) 1.28589E-1(B1) 2.22239E-2(B1) 7.75469E-2(C1) 1.33844E-1(C1) K2 4.17796E-2(C1) 4.44155E-2(C1) 8.88606E-2(C1) 1.64329E-1(C1) 4.38371E-2(C1) 8.21800E-2(B1) 1.60137E-1(B1) K 3 5.63311E-2(D1) 5.87749E-2(D1) 1.00914E-1(D1) 1.75125E-1(D1) 5.94120E-2(D1) 1.08135E-1(D1) 1.90148E-1(D1) K4 9.27837E-2(B2) 1.00358E-1(B2) 2.10729E-1(B2) 3.84031E-1(B2) 1.00599E-1(B2) 2.13235E-1(B2) 3.89800E-1(B2) K 5 1.69162E-1(D2) 1.74683E-1(D2) 2.66428E-1(D2) 4.27545E-1(D2) 1.74897E-1(D2) 2.69281E-1(D2) 4.34314E-1(D2) K 6 2.59694E-1(B3) 2.63843E-1(C2) 3.22655E-1(C2) 4.59351E-1(C2) 2.64006E-1(C2) 3.21588E-1(C2) 4.54582E-1(C2) K 7 2.61316E-1(C2) 2.67963E-1(B3) 4.11836E-1(B3) 6.71466E-1(B3) 2.67794E-1(B3) 4.12190E-1(B3) 6.73633E-1(B3) K 8 2.82499E-1(D3) 2.91442E-1(D3) 4.38485E-1(D3) 6.92823E-1(D3) 2.91565E-1(D3) 4.40050E-1(D3) 6.96770E-1(D3)

表五十三 旋轉傾斜梁不同設定角不同轉速的振動頻率 (十字斷面

d × b × t = 14 × 7 × 0 . 35

，

L

_T

d = 20

，

r = 1

，

α = 30

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.35234E-6 3.14265E-5 1.11271E-4 1.35340E-6 2.14842E-5 -1.93321E-4 εb 0.00000E+0 -1.75275E-4 -3.93587E-3 -1.23067E-2 -1.51659E-4 -3.35204E-3 -1.02901E-2 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.21607E-5 5.63737E-4 1.95171E-3 Utip 0.00000E+0 -6.22310E-6 -3.12800E-3 -2.25083E-2 -4.49377E-6 -2.42982E-3 -2.04420E-2

Vtip 0.00000E+0 -3.49768E-3 -7.43572E-2 -1.99564E-1 -3.02618E-3 -6.48962E-2 -1.79076E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 2.21844E-4 8.80488E-3 6.07220E-2

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -7.66452E-5 -9.50212E-2 -4.50481E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -5.42240E-4 -3.66327E-1 -1.74330E+0

K1 1.48090E-2(B1) 1.48615E-2(B1) 1.61121E-2(B1) 1.96718E-2(B1) 1.48694E-2(B1) 1.60303E-2(B1) 1.94857E-2(B1) K2 4.17796E-2(C1) 4.17424E-2(C1) 3.16498E-2(C1) 2.68475E-2(C1) 4.17564E-2(C1) 3.28302E-2(C1) 2.83831E-2(C1) K 3 5.63311E-2(D1) 5.64218E-2(D1) 6.93781E-2(D1) 7.97805E-2(D1) 5.64056E-2(D1) 6.79486E-2(D1) 8.07173E-2(D1) K4 9.27837E-2(B2) 9.28535E-2(B2) 9.44736E-2(B2) 9.93842E-2(B2) 9.28551E-2(B2) 9.46624E-2(B2) 1.00819E-1(C1) K 5 1.69162E-1(D2) 1.69266E-1(D2) 1.88013E-1(D2) 1.95446E-1(D2) 1.69253E-1(D2) 1.85430E-1(D2) 1.95555E-1(D2) K 6 2.59694E-1(B3) 2.59767E-1(B3) 2.57578E-1(C2) 2.64741E-1(B3) 2.59767E-1(B3) 2.53766E-1(B3) 2.64146E-1(B3) K 7 2.61316E-1(C2) 2.61305E-1(C2) 2.61186E-1(B3) 2.87858E-1(C2) 2.61314E-1(C2) 2.65241E-1(C2) 2.96008E-1(C2) K 8 2.82499E-1(D3) 2.82642E-1(D3) 3.00878E-1(D3) 3.51452E-1(D3) 2.82628E-1(D3) 2.98592E-1(D3) 3.57082E-1(D3)

表五十四 旋轉傾斜梁不同設定角不同轉速的振動頻率 (十字斷面

d × b × t = 14 × 7 × 0 . 35

，

L

_T

d = 20

，

r = 1

，

α = 30

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.35447E-6 1.79450E-5 -3.58430E-4 1.35667E-6 3.35497E-5 1.30114E-4 εb 0.00000E+0 -1.23721E-4 -2.68622E-3 -7.91955E-3 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 3.13125E-5 7.89048E-4 2.78269E-3 4.42051E-5 1.08912E-3 4.17021E-3 Utip 0.00000E+0 -2.77104E-6 -1.68836E-3 -1.75580E-2 6.54692E-7 -4.76378E-5 -8.59565E-4

Vtip 0.00000E+0 -2.46850E-3 -5.34672E-2 -1.54522E-1 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 3.13324E-4 1.10422E-2 7.99162E-2 4.41953E-4 1.08135E-2 4.05185E-2

) 1

1(

Θ 0.00000E+0 -8.80087E-5 -1.14318E-1 -6.30666E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 -6.24344E-4 -4.39965E-1 -2.35848E+0 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.48090E-2(B1) 1.48773E-2(B1) 1.59586E-2(B1) 1.93135E-2(B1) 1.48932E-2(B1) 1.58039E-2(B1) 1.48090E-2(B1) K2 4.17796E-2(C1) 4.17703E-2(C1) 3.43608E-2(C1) 2.87459E-2(C1) 4.17982E-2(C1) 4.22446E-2(C1) 3.69445E-2(D1) K 3 5.63311E-2(D1) 5.63895E-2(D1) 6.58578E-2(D1) 8.11750E-2(D1) 5.63573E-2(D1) 5.50966E-2(D1) 4.36368E-2(C1) K4 9.27837E-2(B2) 9.28566E-2(B2) 9.48370E-2(B2) 1.02892E-1(B2) 9.28598E-2(B2) 9.50493E-2(B2) 1.01980E-1(B2) K 5 1.69162E-1(D2) 1.69239E-1(D2) 1.81760E-1(D2) 1.93489E-1(D2) 1.69213E-1(D2) 1.68492E-1(D2) 1.45392E-1(D2) K 6 2.59694E-1(B3) 2.59767E-1(B3) 2.52484E-1(B3) 2.64267E-1(B3) 2.59768E-1(B3) 2.60247E-1(B3) 2.53033E-1(B3) K 7 2.61316E-1(C2) 2.61323E-1(C2) 2.66900E-1(C2) 3.02492E-1(C2) 2.61341E-1(C2) 2.61933E-1(C2) 2.63746E-1(C2) K 8 2.82499E-1(D3) 2.82614E-1(D3) 2.95466E-1(D3) 3.60884E-1(D3) 2.82585E-1(D3) 2.84808E-1(D3) 2.86639E-1(D3)

表五十五 旋轉傾斜梁不同設定角不同轉速的振動頻率 (十字斷面

d × b × t = 14 × 7 × 0 . 35

，

L

_T

d = 20

，

r = 1

，

α = 45

^o)

0

o

β = β = ³⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.19003E-6 2.48147E-5 6.74592E-5 1.19207E-6 -1.08329E-5 -5.13613E-4 εb 0.00000E+0 -2.48096E-4 -5.65930E-3 -1.80158E-2 -2.14669E-4 -4.82954E-3 -1.53191E-2 εc 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.13431E-5 7.88746E-4 2.62571E-3 Utip 0.00000E+0 -1.33242E-5 -6.55099E-3 -4.91136E-2 -9.85896E-6 -5.35234E-3 -4.60192E-2

Vtip 0.00000E+0 -4.95208E-3 -1.07288E-1 -2.92086E-1 -4.28479E-3 -9.53117E-2 -2.61308E-1 Wtip 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 3.14229E-4 1.66234E-2 1.04156E-1

) 1

1(

Θ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -2.84575E-4 -1.76605E-1 -5.54107E-1 )

1 . 0

1(

Θ′ 0.00000E+0 0.00000E+0 0.00000E+0 0.00000E+0 -1.32663E-3 -6.76169E-1 -2.19708E+0

K1 1.48090E-2(B1) 1.48532E-2(B1) 1.59698E-2(B1) 1.94475E-2(B1) 1.48606E-2(B1) 1.57747E-2(B1) 1.94052E-2(B1) K2 4.17796E-2(C1) 4.16722E-2(C1) 2.76706E-2(C1) 2.47127E-2(C1) 4.17028E-2(C1) 2.88750E-2(C1) 2.63691E-2(C1) K 3 5.63311E-2(D1) 5.64936E-2(D1) 7.39329E-2(D1) 8.29481E-2(D1) 5.64581E-2(D1) 7.30259E-2(D1) 8.44362E-2(D1) K4 9.27837E-2(B2) 9.28460E-2(B2) 9.42458E-2(B2) 9.85134E-2(B2) 9.28478E-2(2) 9.46285E-2(B2) 1.00199E-1(B2) K 5 1.69162E-1(D2) 1.69315E-1(D2) 1.95627E-1(D2) 1.81860E-1(D2) 1.69287E-1(D2) 1.94429E-1(D2) 1.83770E-1(D2) K 6 2.59694E-1(B3) 2.59759E-1(B3) 2.60614E-1(B3) 2.61434E-1(B3) 2.59758E-1(B3) 2.53583E-1(B3) 2.65484E-1(B3) K 7 2.61316E-1(C2) 2.61265E-1(C2) 2.63658E-1(C2) 3.04493E-1(C2) 2.61284E-1(C2) 2.70267E-1(C2) 3.10184E-1(C2) K 8 2.82499E-1(D3) 2.82694E-1(D3) 3.11852E-1(D3) 3.94052E-1(D3) 2.82665E-1(D3) 3.09885E-1(D3) 4.01545E-1(D3)

表五十六 旋轉傾斜梁不同設定角不同轉速的振動頻率 (十字斷面

d × b × t = 14 × 7 × 0 . 35

，L_T d =20，

r = 1

，

α = 45

^o)

45

o

β = β = ⁹⁰

^o

k

0.00000E+0 1.00000E-3 5.00000E-3 1.00000E-2 1.00000E-3 5.00000E-3 1.00000E-2

ε0 0.00000E+0 1.19420E-6 -2.79383E-5 -8.33954E-4 1.19871E-6 2.92312E-5 1.08569E-4 εb 0.00000E+0 -1.75124E-4 -3.87096E-3 -1.20289E-2 0.00000E+0 0.00000E+0 0.00000E+0 εc 0.00000E+0 4.42872E-5 1.10905E-3 3.77792E-3 6.25225E-5 1.54442E-3 5.95473E-3 Utip 0.00000E+0 -6.40596E-6 -3.96518E-3 -4.14863E-2 4.63514E-7 -1.17362E-4 -1.85093E-3

Vtip 0.00000E+0 -3.49538E-3 -8.04627E-2 -2.25467E-1 0.00000E+0 0.00000E+0 0.00000E+0 Wtip 0.00000E+0 4.43594E-4 2.06315E-2 1.39776E-1 6.25106E-4 1.53455E-2 5.79951E-2

) 1

1(

Θ 0.00000E+0 -3.27680E-4 -2.25667E-1 -8.00126E-1 0.00000E+0 0.00000E+0 0.00000E+0 )

1 . 0

1(

Θ′ 0.00000E+0 -1.52858E-3 -8.57245E-1 -3.04865E+0 0.00000E+0 0.00000E+0 0.00000E+0

K1 1.48090E-2(B1) 1.48681E-2(B1) 1.55564E-2(B1) 1.93711E-2(B1) 1.48830E-2(B1) 1.43215E-2(B1) 1.48090E-2(B1) K2 4.17796E-2(C1) 4.17336E-2(C1) 3.02060E-2(C1) 2.67276E-2(C1) 4.17952E-2(C1) 4.21735E-2(C1) 2.27026E-2(C1) K 3 5.63311E-2(D1) 5.64226E-2(D1) 7.14143E-2(D1) 8.50706E-2(D1) 5.63514E-2(D1) 5.30062E-2(D1) 4.33921E-2(D1) K4 9.27837E-2(B2) 9.28496E-2(B2) 9.50300E-2(B2) 1.02844E-1(B2) 9.28532E-2(B2) 9.52441E-2(B2) 9.46765E-2(B2) K 5 1.69162E-1(D2) 1.69259E-1(D2) 1.91941E-1(D2) 1.80351E-1(D2) 1.69204E-1(D2) 1.66257E-1(D2) 1.09384E-1(D2) K 6 2.59694E-1(B3) 2.59758E-1(B3) 2.49313E-1(B3) 2.71014E-1(B3) 2.59758E-1(B3) 2.58774E-1(B3) 2.39497E-1(B3) K 7 2.61316E-1(C2) 2.61302E-1(C2) 2.73036E-1(C2) 3.14249E-1(C2) 2.61338E-1(C2) 2.61864E-1(C2) 2.63443E-1(C2) K 8 2.82499E-1(D3) 2.82635E-1(D3) 3.06267E-1(D3) 4.10144E-1(D3) 2.82577E-1(D3) 2.84658E-1(D3) 2.70942E-1(D3)

圖一 無傾斜角的旋轉梁結構

R

A O

X

₁G

Ω

L

T

A O

_G

X

₁

Ω β

X

₃G

X

₂^G

X

₃G

X

₂^G

β Ω

O

圖二 具傾斜角的旋轉梁結構

圖三 旋轉傾斜梁的上視圖

R α

L

T

A

O X

₁^G

X

₂G

β Ω

R

O A

α β

X

₁G

X

₃G

X

₂G

b a

b

圖四 旋轉傾斜梁的側視圖

圖五 旋轉向量圖

O

β β

X

₃G

X

₂G

Ω

`

圖六 梁之位移以及座標系統關係圖

X

₂G

X

₃G

x

1

x

2

x

3

s

1

2

x x

p

u P

P

X

₁G

) 0 , 0 , (l

v w

O

o

P Q z

y

x

₂S

x

₃S

圖七 梁的斷面圖

t _w t _f t _f

d

b b

t d

b

t a

b

X 2 ^S

X S ₃

X S ₂

X ^S ₂

X ^S ₃

X ^S ₃

0.000 0.005 0.010 0.00

0.01 0.02 0.03 0.04 0.05

N atu ra l F re q u en cy K

β 0^o 45^o 90^o

Angular Speed k

B1 B2

圖八 轉速–(B1、B2)自然頻率圖

(橢圓斷面 a b = 10

，

L

_T

a = 50

，

r = 1

，

α = 45

^o，

N = ⁵⁰ )

0.000 0.005 0.010

-2 -1 0 1

Angular Speed k N o rm al iz ed d et K

T

圖九 轉速–

det K

_T圖

(

橢圓斷面

a b = 10

，

L

_T

a = 50

，

r = 1

，

α = 45

^o、

β = ⁹⁰

^o，

N = ⁵⁰ )

0.0 0.2 0.4 0.6 0.8 1.0 0

2 4 6

D is p la ce m en t( 1 0

d

)

X

^G₁

/L

_T

Line 1 2 3 Disp U

_s

θ

_s1

θ

_s1,x

d -3 -1 -1

2

3 1

2 3

1

k 0.1 0.05

圖十 位移分佈圖

= = = β = ° α =

^o

=

0.0 0.2 0.4 0.6 0.8 1.0 0

1 2 3

3 2

1 4

D is p la ce m en t( 1 0

d

)

Line 1 2 3 4 Disp -U

_s

-V

_s

W

_s

- θ

_s1,x

d -2 -1 -2 -1

1

3

2 4

k 0.01 0.005

X

^G₁

/L

_T

圖十一 位移分佈圖

(橢圓斷面 a b = 10

，

L a = 20

，

r = 1

，

β = 45

^o，

α = ³⁰

^o，

N = ^{35 *} )

0.0 0.2 0.4 0.6 0.8 1.0 0

1 2 3 4

1 Line 1 2 3 4

Disp -U

_s

-V

_s

W

_s

- θ

_s1,x

d -1 -1 -1 0

D is p la ce m en t( 1 0

d

)

3 2

4 1

3 2

4

X

^G₁

/L

_T

k 0.01 0.005

圖十二 位移分佈圖

= = = β =

^o

α =

^o

=

0.00 0.02 0.04 0.06 0.08 0.10 0.0

0.1 0.2 0.3 0.4 0.5 0.6

C1 B1

N at u ra l F re q u en cy K

Angular Speed k B2

B3

C2 B4

D1 β 0

^o

45

^o

90

^o

圖十三 轉速–自然頻率圖

(橢圓斷面 a b = 5

，

L a = 50

，

r = 0

，

α = 0

^o，

N = ²⁰ )

0.00 0.02 0.04 0.06 0.08 0.10 0.0

0.2 0.4 0.6 0.8 1.0

N at u ra l F re q u en cy K

Angular Speed k C1

B1 B2

B3 B4 C2

D1

β 0

^o

45

^o

90

^o

圖十四 轉速–自然頻率圖

= = = α =

^o

=

0.000 0.002 0.004 0.006 0.008 0.010 0.0

0.1 0.2 0.3 0.4 0.5

N at u ra l F re q u en cy K

Angular Speed k β

0

^o

45

^o

90

^o

D1

B4 C2

B3

C1 B2 B1

圖十五 轉速–自然頻率圖

(橢圓斷面 a b = 5

，

L a = 50

，

r = 1

，

α = 30

^o，

N = ^{35 *} )

0.000 0.002 0.004 0.006 0.008 0.010 0.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

B5

N at u ra l F re q u en cy K

Angular Speed k β

0

^o

45

^o

90

^o

B1 C1 B2

B3

C2

B4

D1

圖十六 轉速–自然頻率圖

= = = α =

^o

=

0.000 0.002 0.004 0.006 0.008 0.010 0.0

0.1 0.2 0.3 0.4

N at u ra l F re q u en cy K

Angular Speed k B5

B1 C1 B2

B3 C2

B4 D1

β 0

^o

45

^o

90

^o

圖十七 轉速–自然頻率圖

(橢圓斷面 a b = 10

，

L a = 50

，

r = 1

，

α = 30

^o，

N = ^{35 *} )

0.000 0.002 0.004 0.006 0.008 0.010 0.0

0.1 0.2 0.3 0.4

N at u ra l F re q u en cy K

β 0

^o

45

^o

90

^o

C2

B5 D1

B4

B3 C1 B2 B1

Angular Speed k

圖十八 轉速–自然頻率圖

= = = α =

^o

=

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0 B1

M o d al d ef le ct io n

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-0.4 -0.2 0.0 0.2 0.4 B2

M o d al d ef le ct io n

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

圖十九 傾斜旋轉梁不同設定角不同轉速下的第一、第二振動模態 (橢圓斷面

a b = 10

，

r = 1

，

L a = 20

，

α = 30

^o，

β = ⁰

^o，

N = ^{35 *}

)

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0

C1

M o d al d ef le ct io n

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-0.2 -0.1 0.0 0.1 0.2 B3

M o d al d ef le ct io n

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

圖二十 傾斜旋轉梁不同設定角不同轉速下的第三、第四振動模態

= = = α =

^o

β =

^o

=

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0

D1

M o d al d ef le ct io n

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-0.2 -0.1 0.0 0.1 0.2 B4

M o d al d ef le ct io n

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

圖二十一 傾斜旋轉梁不同設定角不同轉速下的第五、第六振動模態 (橢圓斷面

a b = 10

，

r = 1

，

L a = 20

，

α = 30

^o，

β = ⁰

^o，

N = ^{35 *}

)

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0

M o d al d ef le ct io n

B1

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-0.4 -0.2 0.0 0.2 0.4

M o d al d ef le ct io n

B2

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

圖二十二 傾斜旋轉梁不同設定角不同轉速下的第一、第二振動模態

= = = α =

^o

β =

^o

=

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0

M o d al d ef le ct io n

C1

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-0.2 -0.1 0.0 0.1 0.2

M o d al d ef le ct io n

B3

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

圖二十三 傾斜旋轉梁不同設定角不同轉速下的第三、第四振動模態 (橢圓斷面

a b = 10

，

r = 1

，

L a = 20

，

α = 30

^o，

β = ⁴⁵

^o，

N = ^{35 *}

)

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0

M o d al d ef le ct io n

D1

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-0.2 -0.1 0.0 0.1 0.2

M o d al d ef le ct io n

B4

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

圖二十四 傾斜旋轉梁不同設定角不同轉速下的第五、第六振動模態

= = = α =

^o

β =

^o

=

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0

M o d al d ef le ct io n

B1

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-0.4 -0.2 0.0 0.2 0.4

M o d al d ef le ct io n

B2

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

圖二十五 傾斜旋轉梁不同設定角不同轉速下的第一、第二振動模態 (橢圓斷面

a b = 10

，

r = 1

，

L a = 20

，

α = 30

^o，

β = ⁹⁰

^o，

N = ^{35 *}

)

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0

M o d al d ef le ct io n

C1

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-0.4 -0.2 0.0 0.2 0.4

M o d al d ef le ct io n

B3

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

圖二十六 傾斜旋轉梁不同設定角不同轉速下的第三、第四振動模態

= = = α =

^o

β =

^o

=

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0

M o d al d ef le ct io n

D1

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-0.2 -0.1 0.0 0.1 0.2

M o d al d ef le ct io n

B4

k 0 0.005 0.01 U V W Φ₁

X

^G₁

/L

_T

圖二十七 傾斜旋轉梁不同設定角不同轉速下的第五、第六振動模態 (橢圓斷面

a b = 10

，

r = 1

，

L a = 20

，

α = 30

^o，

β = ⁹⁰

^o，

N = ^{35 *}

)

0.0 0.2 0.4 0.6 0.8 1.0 -1

0 1 2 3 4 5

X

^G₁

/L

_T

Line 1 2 3 4 Disp -U

_s

-V

_s

W

_s

- θ

_s1,x

d -2 -2 -2 -1

D is p la ce m en t( 1 0

d

)

k 0.03 0.01

1 2

1

3 2

3

4 4

圖二十八 位移分佈圖

× = = β =

^o

α =

^o

=

0.0 0.2 0.4 0.6 0.8 1.0 0

1 2 3 4 5 6 7

D is p la ce m en t( 1 0

d

)

Line 1 2 3 4 Disp -U

_s

-V

_s

W

_s

- θ

_s1,x

d -3 -1 -2 -1

X

^G₁

/L

_T

k 0.01 0.005

2 3

2

4 1 3

1 4

圖二十九 位移分佈圖

( I 型斷面 W 10 × 30

，

L d = 25

，

r = 1

，

β = 45

^o，

α = ³⁰

^o，

N = ⁵⁰ )

0.00 0.02 0.04 0.06 0.08 0.10 0.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

D3

N at u ra l F re q u en cy K

Angular Speed k β

0

^o

45

^o

90

^o

C2 B3

D1 D2

C1 B2

B1

圖三十 轉速–自然頻率圖

× = = α =

^o

=

0.00 0.01 0.02 0.03 0.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

N at u ra l F re q u en cy K

Angular Speed k β

0

^o

45

^o

90

^o

D3

C2 B3

D2

B2 D1

C1 B1

圖三十一 轉速–自然頻率圖

( I 型斷面 W 10 × 30

，

L d = 25

，

r = 1

，

α = 5

^o，

N = ⁵⁰ )

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0

B1

M o d al d ef le ct io n

k 0 0.01 0.03 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-1.0 -0.5 0.0 0.5 1.0

C1

M o d al d ef le ct io n

X

^G₁

/L

_T

k 0 0.01 0.03 U V W Φ₁

圖三十二 傾斜旋轉梁不同設定角不同轉速下的第一、第二振動模態

× = = α =

^o

β =

^o

=

0.0 0.5 1.0 -1.0

-0.5 0.0 0.5 1.0

D1

M o d al d ef le ct io n

X

^G₁

/L

_T

k 0 0.01 0.03 U V W Φ₁

0.0 0.5 1.0

-0.2 -0.1 0.0 0.1 0.2 B2

M o d al d ef le ct io n

k 0 0.01 0.03 U V W Φ₁

X

^G₁

/L

_T

圖三十三 傾斜旋轉梁不同設定角不同轉速下的第三、第四振動模態 (I 型斷面

W 10 × 30

，

r = 1

，

L d = 25

，

α = 5

^o，

β = ⁰

^o，

N = ⁵⁰

)

0.0 0.5 1.0 -0.2

-0.1 0.0 0.1

0.2 D2

M o d al d ef le ct io n

k 0 0.01 0.03 U V W Φ₁

X

^G₁

/L

_T

0.0 0.5 1.0

-0.2 -0.1 0.0 0.1 0.2

X

^G₁

/L

_T

B3

M o d al d ef le ct io n

k 0 0.01 0.03 U V W Φ₁

圖三十四 傾斜旋轉梁不同設定角不同轉速下的第五、第六振動模態

圖三十四 傾斜旋轉梁不同設定角不同轉速下的第五、第六振動模態

在文檔中 以有限元素法分析三維旋轉傾斜尤拉梁的穩態變形與自由振動 (頁 80-200)