An Unusual Phenomenon in the Complex Mode Orthogonality Theory and the Strategy Against It

ZHANG Miao; YU Lan>; JU Wei

doi:10.3879/j.issn.1000-0887.2014.10.002

Volume 35 Issue 10

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2014 > 35(10): 1081-1091

ZHANG Miao, YU Lan>, JU Wei. An Unusual Phenomenon in the Complex Mode Orthogonality Theory and the Strategy Against It[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1081-1091. doi: 10.3879/j.issn.1000-0887.2014.10.002

Citation:

PDF( 585 KB)

An Unusual Phenomenon in the Complex Mode Orthogonality Theory and the Strategy Against It

doi: 10.3879/j.issn.1000-0887.2014.10.002

¹School of Science, Changchun Institute of Technology, Changchun 130012, P.R.China;²R&D Center, China FAW Group Corporation, Changchun 130011, P.R.China

Received Date: 2014-04-18
Publish Date: 2014-10-15

Abstract

Abstract

The label phenomenon was revealed through verification of the correctness of the complex mode orthogonality theory used in engineering with numerical experiment. Firstly, the decoupling function of the state vectors under different state space schemes was theoretically analyzed. The related conclusions were also proposed on the orthogonal properties of the state vectors in the cases of symmetric and asymmetric structures with repeated frequencies. Secondly, the label phenomenon was found out and the method to eliminate its undesirable influence was given. Finally, through a general example of sensitivity analysis, the likely risk out of ignorance of the label phenomenon was demonstrated. The research indicates that, through necessary orthogonality check and adjustment of the state vectors’ orders, the decoupling of the state vectors is realized and the adverse effect of the label phenomenon on the calculation accuracy is eliminated.
- complex mode theory,
- label phenomenon,
- orthogonal property,
- decouple,
- diagonalization

FullText(HTML)

References(13)

References

[1]	张淼, 于澜, 鞠伟. 基于松弛技术的重频密频结构模态灵敏度分析[J]. 合肥工业大学学报（自然科学版）, 2012,35(12): 1605-1609.（ZHANG Miao, YU Lan, JU Wei. Modes sensitivity analysis for multiple frequencies and closely spaced modes structure based on relaxation technique[J].Journal of Hefei University of Technology(Natural Sciences),2012,35(12): 1605-1609.（in Chinese））
[2]	张淼, 于澜, 鞠伟. 亏损振系广义状态向量灵敏度的移频算法[J]. 计算力学学报, 2013,30(6): 872-878.（ZHANG Miao, YU Lan, JU Wei. Moving-frequency algorithm of generalized eigenvector sensitivity for defective dynamic system[J].Chinese Journal of Computational Mechanics,2013,30(6): 872-878.（in Chinese））
[3]	盛严, 龚靖, 杨正光. 主动杆系结构的模态性质分析[J]. 噪声与振动控制, 2010,30(5): 6-9, 24.（SHENG Yan, GONG Jing, YANG Zheng-guang. Modal analysis of active framed structure[J].Noise and Vibration Control,2010,30(5): 6-9, 24.（in Chinese））
[4]	解惠青, 戴华. 阻尼系统重特征对导数的计算[J]. 应用数学和力学, 2007,28(6): 749-756.（XIE Hui-qing, DAI Hua. Derivatives of repeated eigenvalues and corresponding eigenvectors of damped systems[J].Applied Mathematics and Mechanics,2007,28(6): 749-756.（in Chinese））
[5]	夏品奇, James M W B. 斜拉桥有限元建模与模型修正[J]. 振动工程学报, 2003,16(2): 219-223.（XIA Pin-qi, James M W B. Finite element modeling and model updating of a cable-stayed bridge[J].Journal of Vibration Engineering,2003,16(2): 219-223.（in Chinese））
[6]	Sondipon A. Rates of change of eigenvalues and eigenvectors in damped dynamic system[J].AIAA Journal,1999,39(11): 1452-1458.
[7]	Sondipon A, Friswell M I. Eigenderivative analysis of asymmetric non-conservative systems [J].International Journal for Numerical Methods in Engineering,2001,51(6): 709-733.
[8]	许鑫, 史治宇. 用于时变系统参数识别的状态空间小波方法[J]. 工程力学, 2011,28(3): 23-28.（XU Xin, SHI Zhi-yu. Parameter identification for time-varying system using state space and wavelet method[J].Engineering Mechanics,2011,28(3): 23-28.（in Chinese））
[9]	于澜, 张淼, 鞠伟, 谷涛. 非保守系统复模态的规范正交性及其应用[J]. 华南师范大学学报（自然科学版）, 2013,45(4): 13-17.（YU Lan, ZHANG Miao, JU Wei, GU Tao. The orthogonality and normalization relationships with its application of complex modes for non-conservative system[J].Journal of South China Normal University (Natural Sciences Edition),2013,45(4): 13-17.（in Chinese））
[10]	李德葆, 陆秋海. 实验模态分析及其应用[M]. 北京: 科学出版社, 2001.（LI De-bao, LU Qiu-hai.Experimental Mode Analysis and Application[M]. Beijing: Science Press, 2001.（in Chinese））
[11]	Greco A, Santini A. Comparative study on dynamic analysis of non-classically damped linear system[J].Structural Engineering and Mechanics,2002,14(6): 679-698.
[12]	沈继红, 胡波, 王侃, 金鑫. 二阶振动系统的解耦条件及算法研究[J]. 振动与冲击, 2012,31(18): 89-92, 156.（SHEN Ji-hong, HU Bo, WANG Kan, JIN Xin. Decouplin coupling and algorithm of a quadratic system[J].Journal of Vibration and Shock,2012,31(18): 89-92, 156.（in Chinese））
[13]	Ward H, Stefan L, Paul S.Modal Analysis Theory and Testing[M]. Brussel, Belgium: Katholieke Universiteit Levven, 1997.