臺灣博碩士論文加值系統

本研究的目標在於提出新的模態參數估測法則，解決目前對於高阻尼與高藕合系統模態分析，仍然不精確的問題。延續Zero Order估測法中最具代表性的CMIF方法，保留其可以指示模所在位置的優點，進而運用頻率響應函數矩陣做奇異值分解後的資料，透過奇異峰值所在位置與左右鄰近點的資料，利用基因演算法或聯立方程式組可以直接求得單一振模之自然頻率與阻尼比。數值模擬的結果顯示出在高耦合情形下，採用本文的方法作參數估測將可以獲得較為精確的結果，在阻尼比高於5％的情況下，結果也較CMIF精確。然而，在阻尼比低與振模之奇異值具有藕合的情況下，CIMF的估測結果是較佳的，因此，模態之分佈情形對估測結果是具有一定的影響性。因應此現象，本研究亦提供判斷模態分佈情形的初步構想，將可作為未來運用奇異值分解技術發展參數估測法的方針。

The purpose of this paper is to develop two new parameter estimation algorithms that can improve the inaccurate results for a highly damped and highly coupled system. Among the zero order algorithms, the most popular one is the Complex Mode Indication Function (CMIF), which features the direct indication of the modes. These two new algorithms, Genetic algorithm and Equation formula algorithm, are developed by preserving the advantage of CMIF and by using the information around the peak of the singular value plot. A highly damped and highly coupled lumped system is chosen for numerical simulation. The results show that the new algorithms can more precisely estimate the highly coupled mode than the CMIF does. For damping ratio higher than 5%, the new algorithms still do the better results as well. However, for lightly damped system and closely coupled singular value plot, the CMIF will have more accurate results than the new algorithms. Under these circumstances, this paper presents a preliminary concept to direct how to properly utilize the parameter estimation algorithm by analyzing the mode distribution situation.

目錄
中文摘要ii
Abstractii
感謝iv
目錄v
圖目錄vii
表目錄ix
第一章 緒論1
1.1前言1
1.2文獻回顧1
1.3 研究動機與目的4
第二章 理論探討5
2.1模態參數估測之基礎理論5
2.2 CMIF模態識別方法17
第三章 應用奇異值分解於模態參數估測23
3.1 應用基因演算法於模態參數之估測23
3.2 採用聯立方程式求解模態參數28
第四章 數值模擬32
4.1 二自由度系統32
4.1.1 二自由度系統之自然頻率估測結果比較35
4.1.2 二自由度系統之阻尼比估測結果比較36
4.2 七自由度系統37
4.2.1 七自由度系統之自然頻率估測結果比較(不含外加雜訊)40
4.2.2 七自由度系統之阻尼比估測結果比較(不含外加雜訊)42
4.2.3 七自由度系統之自然頻率估測結果比較(含5%外加白雜訊)46
4.2.4 七自由度系統之阻尼比估測結果比較(含5%外加白雜訊)48
第五章 結論與未來方向50
參考文獻51
附錄53
附錄一 7自由度系統之MATLAB程式53
附錄二 單一自由度解法之MATLAB程式70
附錄三 聯立方程式解法之MATLAB程式77

[1]Allemang, R.J., Brown, D.L., "Modal Parameter Estimation" Experimental Modal Analysis and Dynamic Component Synthesis, USAF Technical Report, Contract No. F33615-83-C-3218, AFWAL-TR-87-3069,Vol. 3, pp.130, 1987.[2]Brown, D.L., Allemang, R.J., Zimmerman, R.D., Mergeay, M. "Parameter Estimation Techniques for Modal Analysis", SAE Paper No. 790221, SAE Transactions, Vol. 88, pp. 828-846, 1979.[3]Leuridan, J.M., Brown, D.L., Allemang, R.J., "Time Domain Parameter Identification Methods for Linear Modal Analysis: A Unifying Approach", ASME Paper Number 85-DET-90, 1985.[4]Pappa, Richard S., Juang, Jer-Nan, "Galileo Spacecraft Modal Identification Using An Eigensystem Realization Algorithm" AIAA Paper Number 84-1070, 1984.[5]Longman, Richard W., Juang, Jer-Nan, "Recursive Form of the Eigensystem Realization Algorithm for System Identification", AIAA, Journal of Guidance, Control, and Dynamics, Vol. 12, No. 5, pp. 647-652, 1989.[6]Ibrahim, S. R., Mikulcik, E. C. "A Method for the Direct Identification of Vibration Parameters form the Free Response, " Shock and Vibration Bulletin, Vol. 47, Part 4 1977, pp. 183-198.[7]Fukuzono, K., "Investigation of Multiple-Reference Ibrahim Time Domain Modal Parameter Estimation Technique, "M. S. Thesis, Dept. of Mechanical and Industrial Engineering, University of Cincinnati, 1986, 220 pp.[8]Richardson, M., Formenti, D.L., "Parameter Estimation from Frequency Response Measurements Using Rational Fraction Polynomials," Proceedings, International Modal Analysis Conference, pp. 167-182, 1982.[9]Van der Auweraer, H., Leuridan, J., "Multiple Input Orthogonal Polynomial Parameter Estimation", Mechanical Systems and Signal Processing, Vol. 1, No. 3, pp. 259-272, 1987.[10]Coppolino, R. N., "A Simultaneous Frequency Domain Technique for Estimation of Modal Parameters from Measured Data, " SAE Paper No.811046, 1981, 12 pp.[11]Craig, R. R., Kurdila, A.J., Kim, H. M., "State-Space Formulation of Multi-shaker Modal Analysis", Journal of Analytical and Experimental Modal Analysis, Vol. 5, No. 3, 1990, pp. 169-183.[12]Zhang, L., Kanda, H., Brown, D.L., Allemang, R.J. "A Polyreference Frequency Domain Method for Modal Parameter Identification," ASME Paper No. 85-DET-106, pp. 8, 1985.[13]C. Y. Shin, "Investigation of numerical conditioning in the frequency domain modal parameter estimation methods", Ph. D Dissertation, Department of Mechanical and Industrial Engineering, University of Cincinnati, 1989.[14]C. Y. Shin, Y. G. Tsuei, R. J. Allemang, D. L. Brown, "Complex Mode Indication Function and its applications to spatial domain parameter estimation", paper, Department of Mechanical and Industrial Engineering, University of Cincinnati.[15]"Vibration Modal Analysis", Structural Dynamics Research Lab (UC-SDRL),CN-20-263-663/664,June 7,1999