建議

1. 於進行移動荷重試驗過程當中，發現試驗載重車較多的時候，較難維持 試驗的一致性，因此未來在規劃類似的實驗時，建議盡量避免較難掌 控的試驗。

2. 由頻率識別結果可看出，以有限元素分析架構之模型與實際施工完成之 橋體，其結構特性有明顯之差異，可根據識別之結果進一步調整有限 元素分析模型之結構參數，以期能如實反映橋體之動態特性。

3. 本研究礙於量測系統之關係，無法對橋塔部份進行量測及模態識別，建 議日後可採用無線式感應子對橋塔進行量測及分析，並與本研究做一 比較。

4. 弦理論公式並未考慮鋼纜之撓曲剛度及中垂效應，中垂效應較大或撓曲 效應影響較明顯的鋼纜，可能產生較大的誤差；對於長度較長或撓曲效 應影響較明顯的鋼纜，還需進一步確認弦理論公式的適用性。

參考文獻

Aadaleesan, P. and Saha, P., “Nonlinear system identification using laguerre wavelet models”, Chemical Product and Process Modeling, 3(2), Article 3, 2008.

Allemang, R. L. and Brown, D. L., “A correlation coefficient for modal vector analysis”, Proceeding of the first International Modal Analysis Conference, Bethel, Connecticut, U.S.A., 1983.

Bakht, B. and Pinjarkar, S. G., “Review of dynamic testing of highway bridge”, Structural Research Reports, SRR 89-01, Ministry of Transportation of Ontario, Downsview, Ontario, Canada, 1989.

Barbara, B. H., The World According to Wavelets, A . K. Peters Ltd., 1998.

Casas, J. R., “A combined method for estimating cable forces: the cable-stayed Alamillo bridge”, Structural Engineering International, 4(3), 235-240, 1994.

Chui, C. K., An Introduction to Wavelets, Academic Press, Inc., 1992.

Combes, J. M., Grossmann, A. and Tchamitchian Ph. Eds., Wavelet:

Time-Frequency Methods and Phase Space, Springer-Verlag, Berlin, 1990.

Daubechies, I., Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.

Frandrin, P., “Wavelets and related time-scale transforms”, SPIE Advanced Signal-Processing Algorithms, Architectures and Implementation, 1348, 2-13, 1990.

Gersch, W. and Luo, S., “Discrete time series synthesis of randomly excited structural system response”, Acoustical Society of America, Journal, 51, 402-408, 1972.

Ghanem, R. and Romeo, F., “A wavelet-based approach for the identification of linear time-varying dynamical systems”, Journal of Sound and Vibration, 234(4), 555-576, 2000.

Gouttebroze, S. and Lardies, J., “On using the wavelet transform in modal analysis”, Mechanics Research Communications, 28(5), 561-569, 2001.

Huang, C. S., Hung, S. L., Lin, C. I. and Su, W. C., “A wavelet-based approach to identifying structural modal parameters from seismic response and free vibration data”, Computer-Aided Civil and Infrastructure Engineering, 20, 408-423, 2005.

Huang, C. S. and Su, W. C., “Identification of modal parameters of a time invariant linear system by continuous wavelet transformation”, Mechanical Systems and Signal Processing, 21(4), 1642-1664, 2007.

Huang, C. S. and Lin H. L., “Modal identification of structures from ambient vibration, free vibration and seismic response data via a subspace approach”, Earthquake Engineering and Structural Dynamics, 30, 1857-1878, 2001.

Humar, J.L., Dynamics of Structures, Prentice-Hall, Englewood Cliffs, 1990.

Humar, J. L., and Kashif, A. M., “Dynamics response of bridge under travelling loads”, Canadian Journal of Civil Engineering, 20, 287-298, 1993.

Hwang, E. S., Nowak, A. S., “Simulation of dynamic load bridges”, Journal of Structural Engineering, ASCE, 117(5), 1413-1434, 1991.

Lardies, J. and Gouttebroze, S., “Identification of modal parameters using the wavelet transform”, International Journal of Mechanical Sciences, 44, 2263-2283, 2002.

Loh, C. H., Lin, C. Y. and Huang, C. C., “Time domain identification of frames under earthquake loadings”, Journal of Engineering Mechanics, ASCE,

126(7), 693-703, 2000.

Lu, C. J. and Hsu, Y. T., “Vibration analysis of an inhomogeneous string for damage detection by wavelet transform”, International Journal of Mechanical Sciences, 44, 745-754, 2002.

Ovanesova, A. V. and Suarez, L. E., “Applications of wavelet transforms to damage detection in frame structures”, Engineering Structures, 26, 39-49, 2004.

Paulter, P., Chaallal, O. and Proulx, J., “Bridge dynamics and dynamic amplification factors – A review of analytical and experimental findings”, Canadian Journal of Civil Engineering, 19(2), 260-278, 1992.

Paulter, P., Proulx, J. and Talbot, M., “Dynamic test procedure for highway bridge using traffic loads”, Journal of Structural Engineering, ASCE, 121 (2), 362-376, 1995.

Piombo, B., Giorcelli, E., Garibaldi, L. and Fasana, A., “Stuctural identification using ARMAV models”, Proceedings of the 11^th International Modal Analysis Conference, 588-592, 1993.

Strang, G., “Wavelet transforms versus Fourier transforms”, Bulletin of the American Mathematical Society, 28(2), 288-305, 1993.

Triantafyllou, M. S. and Grinfogel, L., “Natural frequecies and modes of inclined cables”, Journal of the Structural Engineering, 112(1), 139-148, 1986.

UrrutiaGalicaia, J. L. and SalazarHernandez, A., “On the maximum amplification factor of a moving point force on a simple beam”, Transactions of the Canadian Society for Mechanical Engineering, 16(1), 61-81, 1992.

Vandiver, J. K., Dunwood, A. B., Campbell, R. B. and Cook, W. F., “A

mathematical bases for the random decrement vibration signature analysis technique”, Journal of Mechanical Design, 104, 307-313, 1982.

Wang, T. L. and Huang, D. Z., “Cable-stayed bridge vibration due to road surface roughness”, Journal of Structural Engineering, ASCE, 118(5), 1354-1374, 1992.

Wang, Z. N. and Fang, T., “A time-domain method for identifying modal parameters”, Transaction of ASME, Journal of Applied Mechanic, 53, 28-32, 1986.

Yule, G. U., “On a method of investigating periodicities in disturbed series, with special reference to Wolfer’s sunspot numbers”, Philosophical Transactions of the Royal Society of London, Series A, 226-267, 1927.

Zui, H., Shinke, T. and Namita, Y., “Practical formulas for estimation of cable tension by vibration method”, Journal of Structural Engineering, ASCE, 122(6), 651-656, 1996.

李政寬、陳建州、周智傑、張國鎮，「斜張鋼纜微振訊號有限元素法解析」，

中國土木水利工程學刊，第 18 卷，第 2 期，第 279-288 頁，2006。

吳文華、陳建州、劉謹銘、黃克耀，「集鹿斜張橋之鋼纜微振量測分析」，

第七屆結構工程研討會論文集，論文編號 G03，2004。

吳文華、廖釗銨、陳建州，「利用單點微振量測之斜張鋼纜多振態參數識 別」，第八屆結構工程研討會論文集，論文編號 Q008，2006。

陳建州、李政寬、周智傑、張國鎮，「斜張鋼纜索力分析之參數研究」，中 國土木水利工程學刊，第 18 卷，第 4 期，第 337-345 頁，2006。

陳振華、黃炯憲、蘇威智、歐嘉宜，「超長跨斜張橋之微動試驗與模態識別」， 第九屆結構工程研討會論文集，論文編號 B-0370，2008。

黃炯憲，「微動量測分析工具探討(二)-時間序列法」，國家地震工程研究中 心報告，NCREE-99-018，1999。

黃炯憲，「西藏大橋衝擊試驗與動力特性識別」，西藏大橋動力及靜力特性 之監測及分析期末報告，第 3-1-3-84 頁，2000。

黃炯憲、葉錦勳、林憲忠、葉公贊，「隨機遞減法在微振量測之應用

－比例阻尼系統」，國家地震工程研究中心研究報告，NCREE-96-013，

1996。

楊加地，「脊背橋動力試驗之模擬分析」，國立交通大學土木工程學系研 究所，碩士論文，2007。

表 2.1 SPC51 規格介紹

型號 SPC51

頻道數 16

A/D 轉換 16bit

最大輸出電壓 ±10V

取樣頻率 可調式(10,20,50,100,200,500,1000Hz) 放大倍率(Gain) 1、2、10、100

啟動方式 手動、自動、時間設定

高通濾波器 0.1Hz 或 1Hz

低通濾波器 ¹

3×取樣頻率

紀錄長度 可調式(最多 99999999 點/頻道)

記憶體 硬碟 9.34G

表 2.2 VSE15D 速度計規格 型號 VSE15D 頻率範圍 0.1~70Hz 量測範圍 ±10cm/sec(kine)

靈敏度 1V/kine 或 10V/kine 最大輸出電壓 ±10V

表 2.3 LVDT 規格介紹

型號 DDP-50A

量測範圍 50mm

輸出電壓 ^{2.5mV V/ ±0.3%}

(5000 10× ⁻⁶strain±0.3%) 靈敏度

100 10× ⁻6strain/mm

非線性現象 ^0.3%RO

感應子彈力 5.4N

頻率響應 1Hz

溫度範圍 ^{0 ~ 60+ C}

輸入/輸出 電阻 ^350Ω

最小激發電壓 Less than 2V

最大激發電壓 5V

重量 500g

表 4.1 微動試驗求取隨機遞減訊號之參考測站 Ambient test

mode f(Hz) damping(%) Impact test

mode f(Hz) damping(%)

表 4.4 有限元素軟體分析出之橋梁動態特性 Finite element method

mode f(Hz) 1 0.75 (x,z) 2 1.02 (x,z) 3 1.45 (x,z) 4 1.92 (x,z) 5 1.94 (y) 6 2.68 (x,z) 7 2.79 (y) 8 2.94 (y) 9 3.26 (x,z) 10 4.29 (x,z)

表 4.5 微動試驗、衝擊試驗、有限元素分析 MAC 值比較

frequency (Hz) MAC

mode

ambient impact FEM ambient VS. impact ambient VS. FEM impact VS. FEM

x-1 1.48 1.47 1.02 0.898 0.866 0.769

x-2 2.09 2.03 1.92 0.861 0.888 0.833

x-3 3.16 3.19 2.68 0.904 0.980 0.917

y-1 1.74 1.71 1.94 0.989 0.952 0.954

y-2 2.62 2.58 2.79 0.877 0.931 0.874

y-3 2.82 2.88 2.94 0.870 0.825 0.661

z-1 0.88 0.93 0.75 0.997 0.993 0.984

z-2 1.48 1.47 1.02 0.857 0.827 0.846

z-3 1.74 1.72 1.45 0.976 0.969 0.938

z-4 2.09 2.03 1.92 0.982 0.972 0.978

z-5 3.51 3.51 3.26 0.978 0.958 0.972

表 4.6 動態車流載重試驗之位移 DAF(一台卡車單向行駛)