本文已經完成，應用最佳化總域極小化反算彈性支撐複合材料板 結構系統參數之方法。混合實驗與理論分析方式，在不破壞結構及其 邊界條件的情形下，以非破壞性方式識別結構之所有系統參數。經由 反算結果與討論，可以得到以下之結論：
1. 針對文中這些不同寬厚比、疊層角度彈性支撐複材積層板試片，反 算結果顯示其材料性質並沒有明顯和寬厚比、疊層角度有關。
2. 彈性支撐複合材料積層厚板與三明治板，由於頻率實驗量測時已有 較大之誤差，所以其反算結果會有較大之誤差產生。
3. 若是沒有對設計變數取單位化和有效上、下限技巧，將可能產生很 差之結果甚至無法收斂。
4. 本文方法具可行性與精確性，並可將此研究方法應用於其他不同類 型材料結構的系統參數識別。
由系統參數識別結果顯示，本文建立之 Ritz 方法對於自然頻率分 析非常精確，且反算方法對於總域極小值之處理非常正確、有效率。
所以，不論是彈性支撐複合材料積層板或是彈性支撐複合材料三明治 板之系統參數識別，皆能應用振動實驗量測其自然頻率之方式來建立 誤差函數，再進行反算程序，且所獲得的結果都是非常精確。
另外，探討複合材料三明治板彈性常數之識別時，因面層與中間 夾心層分屬不同材料，且其勁度差異很大，必須使用分層理論將厚度 方向分成三個（面層兩個與夾心層一個）一階剪變形位移場來分析自
然頻率，此時共有七個位移函數，再加上設計變數增為七個，所以 A.L.M. 總域極小化演算時間與計算機硬體需求將大增；而且複合材料 三明治板，因為其本身面層、心層的材料性質差異很大，彼此間是用 樹脂黏合而成，所以自然振動頻率量測時，會面臨較多的雜訊與困難 參雜其中；另外，邊界彈性支撐是用等效彈簧方式模擬，且以簡單的 材料力學方式推導得到，這樣亦會和實際之情形有所差別。而複合材 料三明治板在自然頻率量測時即有較大的誤差，所以會造成其反算結 果有較大之誤差產生。針對上述問題，是不是可以有（一）更精確、
有效的邊界模擬；（二）更簡單、精確且有效率的自然頻率分析理 論；（三）使用更精確的自然頻率量測儀器設備（如非接觸方式 等）。如此將可有效提昇反算工作之精確及效率，並降低運算時間成 本。這些是值得再研究改善的地方。
參 考 文 獻
1.Reismann, H. and Pawlik, P. S., “Elasticity – Theory and Applications,”
(1969).
2. Reddy, J. N., “Energy and Variational Methods in Applied Mechanics,”
Junuthula Narasimha (1945).
3. Jones, R. M., “Mechnics of Composite Materials,” McGraw-Hill Inc (1975).
4. Gibson, R. F., “Principles of Composite Material Mechanics,”
McGraw-Hill Inc (1994).
5.Mindlin, R. D., “Influence of Rotatory Inertia and Shear Deformation on Flexural Motions of Isotropic, Elastic Plates,” Journal of Applied Mechanics, Vol. 18, pp. 31-38 (1951).
6. Mindlin, R. D., “Influence of Rotatory Inertia and Shear in Flexural Motin of Isotropic, Elastic Plates,” Journal of Applied Mechanics, Vol.
18, pp. 1031-1036 (1951).
7.Whitney, J. M. and Pagano, N. J., “Shear Deformation in Heterogeneous Anisotropic Plates,” Journal of Applied Mechanics, Vol. 37(4), Trans.
ASME, Vol. 92, pp. 1031-1036 (1970).
8. Whitney, J. M., “Stress Analysis of Thick Laminated Composite and Sandwich Plates,” Journal of Composite Materials, Vol. 6, pp. 426-440 (1972).
9. Reddy, J. N., “A Penalty Plate-Bending Element for the Analysis of Laminated Anisotropic Composite Plates,” International Journal for Numerical Methods in Engineering, Vol. 15, pp. 1187-1206 (1980).
10.Reddy, J. N., “A Simple Higher-Order Theory for Laminated Composite Plates,” Journal of Applied Mechanics, 51, pp. 745-752 (1984).
11. Hanna, N. F. and Leissa, A. W., “A Higher Order Shear Deformation Theory for the Vibration of Thick Plates,” Journal of Sound and Vibration, 170(4), pp. 545-555 (1994).
12.Frederiksen, P. S., “Single-Layer Plate Theories Applied to the Flexural Vibration of Completely Free Thick Laminates,” Journal of Sound and Vibration, 186(5), pp. 743-759 (1995).
13. Bardell, N. S., Dunsdon, J. M. and Langley, R. S., “Free Vibration Analysis of Coplanar Sandwich Panels,” Composite Structures, 38, pp.
463-475 (1997).
14.Kant, T. and Swaminathan, K., “Free Vibration of Isotropic, Orthotropic, and Multilaryer Plates Based on Higher Order Refined Theories,”
Journal of Sound and Vibration, 241(2), pp. 319-327 (2001).
15. Kant, T. and Swaminathan, K., “Analytical Solutions for Vibration of Laminated Composite and Sandwich Plates Based on a Higher-Order Refined Theory,” Composite Structures, 53, pp. 73-85 (2001).
16.Nayak, A. K., Moy, S. S. J. and Shenoi, R. A., “Free Vibration Analysis of Composite Sandwich Plates Based on Reddy’s Higher-Order Theory,” Composites: Part B, Vol. 33, pp. 505-519 (2002).
17. Mau, S. T., “A Refined Laminated Plate Theory,” Journal of Applied
Mechanics, Vol. 40(2), pp. 606-607 (1973).
18.周仲彥, “複合材料積層板之線性及非線性變形分析,” 國立交通大學 機械工程研究所碩士論文 (1993)。
19.賴峰民, “複合材料積層板設計及製造,” 國立交通大學機械工程研究 所碩士論文 (1993)。
20. 趙大年, “含剪變形複合材料板之非線性行為研究,” 國立交通大學 機械工程研究所碩士論文 (1994)。
21.廖紹助, “複合材料積層板之輕量設計,” 國立交通大學機械工程研究 所碩士論文 (1994)。
22. Hung, K. C., Lim, M. K. and Liew, K. M., “Boundary Beam Characteristics Orthonormal Polynomials in Energy Approach for Vibration of Symmetric Laminates-II: Elastically Restrained Boundaries,” Composite Structures, Vol. 26, pp. 185-209 (1993).
23. Ding, Z., “Natural Frequencies of Rectangular Plates Using a Set of Static Beam Functions in Rayleigh-Ritz Method,” Journal of Sound and Vibration, Vol. 189(1), pp.81-87 (1996).
24. Narita, Y. and Leissa, A. W., “Frequencies and Mode Shapes of Cantilever Laminated Composite Plates,” Journal of Sound and Vibration, Vol. 154(1), pp.161-172 (1992).
25. Liew, K. M., Hung, K. C. and Lim, M. K., “Vibration of Mindlin Plates Using Boundary Characteristic Orthogonal Polynomials,” Vol. 182(1), pp.77-90 (1995).
26. Liew, K. M., “Solving the Vibration of Thick Symmetric Laminates by Reissner/Mindlin Plate Theory and the P-Ritz Method,” Journal of Sound and Vibration, Vol. 198(3), pp.343-360 (1996).
27. Snyman, J. A. and Fatti, L. P., “A Multi-Start Global Minimization Algorithm with Dynamic Search Trajectories,” Journal of Optimization Theory and Applications, Vol. 54, pp. 121-141, (1987).
28. Kam, T. Y. and Snyman, J. A., “Optimal Design of Laminated Composite Structures Using a Global Optimization Technique,” Journal of Composite Structure, Vol. 19, pp. 351-370 (1991).
29. Vandperplaats, G. N., “Numerical Optimization Techniques for Engineering Design ：with Application,” McGraw-Hill Inc (1993).
30. Aora, J. S., “ Introduction to Optimum Design,” McGraw-Hill Inc., (1989).
31. 徐業良, “工程最佳化設計,” 國立編譯館, (1995)。
32. Deobald, L. R. and Gibson, R. F., “Determination of Elastic Constants of Orthotropic Plates by a Modal Analysis/Rayleigh-Ritz Technique,”
Journal of Sound and Vibration, Vol. 124(2), pp. 269-283 (1988).
33. Frederiksen, P. S., “Estimation of Elastic Moduli Thick Composite Plates by Inversion of Vibrational Data,” Inverse Problem in Engineering Mechanucs, Balkema, Rotterdam, pp. 111-118 (1994).
34.Castagnede, B., Jenkins, J. T., Sachse, W. and Baste, S., “Optimal Determination of the Elastics of Composite Materials from Ultrasonic Wavespeed Measurement,” Journal of Applied Physics, Vol. 66, pp.
2753-2761 (1990).
35. Fallstrom, K. E. and Jonsson, M., “A Nondestructive Method to Determine Material Properties in Anistropic Plate,” Polymer Composites, Vol. 12(5), pp. 293-305 (1991).
36. Nielsen, S. A. and Toftegaard H., “Ultrasnic Measurement of Elastic Constants in Fiber-reinforced Polymer Composites Under Influence of Absorbed Moisture,” International Journal of Ultrasonic, Vol. 38, pp.
242-246 (1998).
37. Berman, A. and Nagy, E. J., “Improvement of a Large Analytical Model Using Test Data,” AIAA J., Vol. 21, pp. 1168-1173 (1983).
38. Kam, T. Y. and Lee, T. Y., “Crack Size Identification Using and Expanded Mode Method,” International Journal of Solids & Structures, Vol. 31, pp. 925-940 (1994).
39. Kam, T. Y. and Lee, T. Y., “Detection of Cracks from Modal Test Data, International Journal of Engineering Fracture Mechanics, Vol. 42, pp.
381-387 (1992).
40. Kam, T. Y. and Lee, T. Y., “Identification of Crack Size via and Energy Approach, Journal of Nondestructive Evaluation, Vol. 13, pp. 1-11 (1994).
41. Kam, T. Y. and Liu, C. K., “Stiffness Identification of Laminated Composite Shafts,” International Journal of Mechanical Sciences, Vol.
40(9), pp. 927-936 (1998).
42. Wang, W. T. and Kam, T. Y., “Material Characterization of Laminated Composite Plates via Static Testing,” International Journal of Composite Structures, Vol. 50(4), pp. 347-352 (2000).
43. Wang, W. T. and Kam, T. Y., “Elastic Constants Identification of Shear Deformable Laminated Composite Plates,” ASCE, Journal of Engineering Mechanics Division, Vol. 127(11), pp.1117-1123 (2001).
44. Booker, L., “Improving Search in Genetic algorithms,” in Davis, L.(Editor), Genetic Algorithms and Simulated Annealing (1987).
45. Kincaid, R. K. and Padula, S. L., “Minimizing Distortion and Internal Forces in Truss Structure by Simulated Annealing,” Proceedings, 31st AIAA /ASME/ASCE/AHS/ASC Structures, Structural Materials and Dynamics Conference, Held in Long Beach, California, Paper No.
AIAA-90-1095-CP, pp. 327-333 (1990).
46. Balling, R. J., “Optimal Steel Frame Design by Simulated Annealing.”
Journal of Structural Engineering, Vol. 117, pp. 1780-1795 (1991).
47.May, S. A. and Balling, R. J., “A Filtered Simulated Annealing Strategy for Discrete Optimization of 3D Steel Frameworks,” Structural Optimization, Vol. 4, pp. 142-148 (1992).
48. Haupt, R. L. and Haupt, S. E., “Practical Genetic Algorithms,” (1988).
49.Goldberg, D. E., “Genetic Algorithms in Search, Optimization and Machine Learning,” (1989).
50. Banzhaf, W., and Reeves, C., “Foundations of Genetic Algorithms,”
(1999).
51.Gen, M. and Cheng, R., “Genetic Algorithms and Engineering Design (Wiley Series in Engineering Design and Automation) ,” (1999).
52.Goldberg, D. E. and Kuo, C. H., “Genetic Algorithms in Pipeline Optimization,” Journal of Computing in Civil Engineering, Vol. 1, pp.
128-141 (1987).
53. Lin, C. Y. and Fleury, C., “Genetic Algorithms in Optimization Problems with Discrete and Integer Design Variables,” Engineering Optimization, Vol. 19, pp. 309-327 (1992).
54. Huang, C. C. and Huang, Y. F., “Bounds on the Numbers of Hidden Neuron in Multiplayer Perceptrons,” IEEE Trans. Neural Networks, Vol. 2(1), pp.47-55 (1991).
55. Salchenberger, Cinar, E. M. and Lash, N. A., “Nueral Networks : A New Tool for Predicting Thrift Failures,” Decision Sciences, Vol. 23, pp889-916 (1992).
56.Sexton, R. S., Dorsey, R. E. and Johnson, J. D., “Toward Global Optimization of Neural Networks : A Comparison of the Genetic Algorithm and Backprogation,” Decision Support System, Vol. 22, pp171-186 (1998).
57. Sexton, R. S., Jatinder N. D. and Gupta, “Comparative Evaluation of Genetic Algorithm and Backpropagation for Training Neural Networks,” Information Sciences 129, pp.45-59 (2000).
58. “ASTM Standards and Literature References for Composite Materials,”
2nd ed., West Conshohocken, Pa (1990).
59. “The ANSYS Release 5.4 User’s Manual,” Analysis Inc, 1997.
60. Masoud, R. R. and Pierre, M., “Buckling and Vibration Analysis of Composite Sandwich Plates with Elastic Rotational EEdge Restraints,”
AIAA Journal, Vol 37(5), pp. 579-587 (1999).
61. Reddy, J. N., “Mechanics of Laminated Composite Plates Theory and
Analysis,” CRC Press, Boca Raton, FL, pp. 332-333 (1997).
62.Reddy, J. N. and Phan, P. H., “Stability and vibration of isotropic, orthotropic and laminated plates according to a higher order shear deformation theory,” Journal of sound and vibration, Vol. 98, pp. 157-170 (1985).
63. Raville, M. E. and Ueng, C. E. S., “Determination of Natural Frequencies of Vibration of a Sandwich Plate.” Exp. Mech., Vol. 7, pp.
490-493 (1967).
64. Zhou, H. B. and Li, G. Y., “Free Vibration Analysis of Sandwich Plates with Laminated Faces Using Spline Finite Point Method,” Computers and structures, Vol. 59(2), pp. 257-263 (1996).
65. Khare, R. K., Kant, T. and Garg, A. K., “Free Vibration of Composite and Sandwich Laminates with a Higher-Order Facet Shell Element,”
Composite Structures, Vol. 65, pp. 405-418 (2004).
66. Watanabe, N., Miyachi, K. and Daimon, M., “Stiffness and Vibration Characteristic of Sandwich Plates with Anisotropic Composite Laminates Face Sheets.” Proc., Conf. on AIAA/ASME/ASCE/AHS/
ASC 34th Structures, Structural Dynamics, and Material Conference, 236-244 (1993).
附 錄 一
k層側向剪應力表示為
附 錄 二
s ymmetric s ymmetric
ω