ON THE REDUNDANCY OF COMPLEX MODAL PARAMETERS

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (12): 1412-1420.

ON THE REDUNDANCY OF COMPLEX MODAL PARAMETERS

陈奎孚, 焦群英

College of Science, China Agricultural University, Beijing 100083, P. R. China

收稿日期:2003-01-15 修回日期:2004-07-06 出版日期:2004-12-18 发布日期:2004-12-18
通讯作者: JIAO Qun-ying, Professor, Doctor Corresponding author,(Tel:+86-10-62736411:Fax:+86-10-62736777:E-mail:jiaoqy@cau.edu.cn) E-mail:jiaoqy@cau.edu.Cn

ON THE REDUNDANCY OF COMPLEX MODAL PARAMETERS

CHEN Kui-fu, JIAO Qun-ying

College of Science, China Agricultural University, Beijing 100083, P. R. China

Received:2003-01-15 Revised:2004-07-06 Online:2004-12-18 Published:2004-12-18

摘要/Abstract

摘要： Generating the simulation transfer function (TF) is indispensable to modal analysis, such as examining modal parameters identification algorithm, and assessing modal analysis software. Comparing 3 feasible algorithms to simulate TF shows that,one of them is preperable,which is expressing the TF as the function of the complex modal parameters(CMPs),because the deliberate behaviors of CMPs can be implemented easily,such as,dense modals,large damping,and complex modal shape,etc.Nonetheless,even this preferable algorithms is elected,the complex modal shapes cannot be specified arbitrarily,because the number of CMPs far more exceeds that in physical coordinate.So for physical realizable system,there are redundant constraints in CMPs.By analyzing the eigenvalue problem of a complex modal system,and the inversion equations from CMPs to physical parameters,the explicit redundancy constraints were presented.For the special cases,such as the real modal,the damping free modal,and non-complete identification,the specific forms of the redundancy constraints were discussed,along with the number of independent parameters.It is worthy of noting that,redundancy constraints are automatically satisfied for the real modal case.Their equivalent forms on the transfer matrix and a column of transfer matrix were also provided. These results are applicable to generate TF, to implement identification by optimization and appreciate the identification results, to evaluate residual modal, and to verify the complementary of identified modal orders.

Abstract: Generating the simulation transfer function (TF) is indispensable to modal analysis, such as examining modal parameters identification algorithm, and assessing modal analysis software. Comparing 3 feasible algorithms to simulate TF shows that,one of them is preperable,which is expressing the TF as the function of the complex modal parameters(CMPs),because the deliberate behaviors of CMPs can be implemented easily,such as,dense modals,large damping,and complex modal shape,etc.Nonetheless,even this preferable algorithms is elected,the complex modal shapes cannot be specified arbitrarily,because the number of CMPs far more exceeds that in physical coordinate.So for physical realizable system,there are redundant constraints in CMPs.By analyzing the eigenvalue problem of a complex modal system,and the inversion equations from CMPs to physical parameters,the explicit redundancy constraints were presented.For the special cases,such as the real modal,the damping free modal,and non-complete identification,the specific forms of the redundancy constraints were discussed,along with the number of independent parameters.It is worthy of noting that,redundancy constraints are automatically satisfied for the real modal case.Their equivalent forms on the transfer matrix and a column of transfer matrix were also provided. These results are applicable to generate TF, to implement identification by optimization and appreciate the identification results, to evaluate residual modal, and to verify the complementary of identified modal orders.

中图分类号:

陈奎孚;焦群英. ON THE REDUNDANCY OF COMPLEX MODAL PARAMETERS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(12): 1412-1420.

CHEN Kui-fu;JIAO Qun-ying . ON THE REDUNDANCY OF COMPLEX MODAL PARAMETERS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(12): 1412-1420.

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