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系統識別號 U0026-0607201112531900
論文名稱(中文) 結構系統非比例阻尼指標之研究
論文名稱(英文) A Study on the Index of Non-proportional Damping in Structural Systems
校院名稱 成功大學
系所名稱(中) 航空太空工程學系碩博士班
系所名稱(英) Department of Aeronautics & Astronautics
學年度 99
學期 2
出版年 100
研究生(中文) 陳奕伸
研究生(英文) Yi-Shan Chen
學號 p46981166
學位類別 碩士
語文別 中文
論文頁數 50頁
口試委員 指導教授-江達雲
口試委員-鄭泗滄
口試委員-崔兆棠
中文關鍵字 非比例阻尼  狀態空間法 
英文關鍵字 non-proportional damping  State Space method 
學科別分類
中文摘要 在模態分析中,為了能夠使用正規模態矩陣解耦系統方程,吾人會假設系統含比例阻尼,解耦後的系統會具有實模態的形式。然而一般含阻尼的線性結構系統會呈現複模態的形式而不是實模態的形式,而複模態形式的產生與阻尼的非比例性有關,因此了解系統阻尼的非比例性程度便成為一個工程上重要的課題。本文主要探討如何定義出可以有效的描述系統中阻尼非比例性的量化指標,首先針對前人所提出的非比例阻尼指標,進行模擬與分析,進而提出兩個新指標,以有效反映系統中阻尼的非比例性程度。再以數值模擬的方式,比較各個指標之間的優劣,驗證本文所提出的新指標之可行性。
英文摘要 In conventional modal analysis of damped systems, the equations of motion can be diagonalized using the undamped modal matrix when the damping matrix is known as proportional damping or classical damping. In general, however, damped linear systems possess complex modes instead of classical normal modes due to non-proportionality of damping, and therefore it is of great interest to study the non-proportionality of damping of general structural systems. This thesis studies how to define appropriate indices to quantify the non-proportionality of damping , which are referred to as the indices of non-proportional damping in the present study. Two new indices measuring the non-proportionality of damping are proposed, the applicability of the proposed indices is demonstrated by numerical simulations. The examples also show the performance of the proposed indices in comparison with existing indices.
論文目次 中文摘要………………………………………………………………Ⅰ
英文摘要………………………………………………………………Ⅱ
誌謝……………………………………………………………………Ⅲ
目錄……………………………………………………………………Ⅳ
表目錄…………………………………………………………………Ⅵ
圖目錄…………………………………………………………………Ⅶ
第一章 緒論…………………………………………………………… 1
1-1 引言…………………………………………………………… 1
1-2 模態分析與系統識別………………………………………… 3
1-3 文獻回顧……………………………………………………… 5
1-4 研究動機與目的……………………………………………… 8
第二章 非比例阻尼系統介紹………………………………………… 9
2-1 引言…………………………………………………………… 9
2-2 正規模態與複模態……………………………………………10
第三章 非比例阻尼指標………………………………………………21
3-1 引言……………………………………………………………21
3-2 第一類指標介紹………………………………………………22
3-3 第二類指標介紹………………………………………………24
3-4 第三類指標介紹………………………………………………27
3-5 第四類指標介紹………………………………………………29
3-6 新指標定義……………………………………………………32
第四章 數值模擬………………………………………………………35
4-1 引言……………………………………………………………35
4-2 直接在矩尼矩陣上加上非比例項……………………………35
4-3 調整模態阻尼矩陣的非對角線項……………………………38
第五章 結論……………………………………………………………40
參考文獻………………………………………………………………42
參考文獻 [1] T. K. Coughey, M E Okely, “Classical normal modes in damped linear dynamic system”, Journal of Applied Mechanics,1965,32, Pages 583~588
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[3] D. J. Ewins, “Modal Testing:Theory and Practice”,Research Studies Press, 1984
[4] K.A. Foss, “Coordinates which uncouple the equations of motion of damped linear dynamic systems”, Transaction of ASME, Journal of Applied Mechanics 25 ,1958 , Pages 361-364
[5] D.E. Newland, “On the modal analysis of nonconservative linear systems”, Journal ofSound and Vibration 112,1987, Pages 69-96
[6] A. Sestieri, R. Ibrahim, “Analysis of errors and approximations in the use of modal coordinates”, Journal of Sound and Vibration 177 (1994) , Pages 145–157
[7] T. K. Haesselman, “Modal coupling in lightly damped structures”, AIAA Journal 14 , 1976,Pages 1627-1628
[8] S. Park, I. Park and F. Ma, “Decoupling approximation of nonclassicaly damped structures”, AIAA Journal 30 ,1992,Pages 2348-2351
[9] E. Balmes, “New results on the identification of normal mode from experimental complex mode”, Mechanical System and Signal Processing 1997 Pages 229-243
[10] G. Prater Jr., R. Singh ,“Quantification of the extent of non-proportional viscous damping in discrete vibratory systems” , Journal of Sound and Vibration, Volume 104, Issue 1, 8 January 1986, Pages 109-125
[11] M. Tong, Z. Liang, G. C. Lee ,“An Index of Damping Non-Proportionality for Discrete Vibrating Systems” , Journal of Sound and Vibration, Volume 174, Issue 1, 30 June 1994, Pages 37-55
[12] Kefu Liu, Marek R. Kujath, Wanping Zheng,“Quantification of non-proportionality of damping in discrete vibratory systems” , Computers & Structures, Volume 77, Issue 5, 21 July 2000, Pages 557-570
[13] Kefu Liu, Marek R. Kujath, Wanping Zheng ,“Evaluation of damping non-proportionality using identified modal information” , Mechanical Systems and Signal Processing, Volume 15, Issue 1, January 2001, Pages 227-242
[14] S. Adhikari ,“Optimal complex modes and an index of damping non-proportionality” ,Mechanical Systems and Signal Processing, Volume 18, Issue 1, January 2004, Pages 1-27
[15] A. Srikantha Phani, “On the necessary and sufficient conditions for the existence of classical normal modes in damped liner dynamic systems”, Journal of Sound and Vibration 264 2003,Pages 741-745
[16] J. Kirshenboim., ”Real vs. complex mode shapes” , Proceeding of 5th International Modal Analysis Conference, London, England, 1987, Pages.1594-1599
[17] S. R. Ibrahim, ”Computation of normal modes from identified complex modes ”, AIAA Journal, Vol.21, No3,1983,Pages 446-451
[18] M. L. Wei., R. J. Allemang. and D. L. Brown, “Real-Normalization of measured complex modes”, Proceedings of 5th International Modal Analysis Conference, London, England 1987, Pages 708-712
[19] A. Sestieri, S.R.Ibrahim, “Analysis of errors and approximations in the use of modal co-ordinates”, Journal of Sound and Vibration 1994 177(2) Pages 145-157
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