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Structural Engineering and Mechanics Volume 42, Number 4, May25 2012 , pages 449-469 DOI: https://doi.org/10.12989/sem.2012.42.4.449 |
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Dynamic response analysis of generally damped linear system with repeated eigenvalues |
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Rui-fang Yu, Xi-yuan Zhou and Mei-qiao Yuan
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| Abstract | ||
| For generally damped linear systems with repeated eigenvalues and defective eigenvectors, this study provides a decomposition method based on residue matrix, which is suitable for engineering applications. Based on this method, a hybrid approach is presented, incorporating the merits of the modal superposition method and the residue matrix decomposition method, which does not need to consider the defective characteristics of the eigenvectors corresponding to repeated eigenvalues. The method derived in this study has clear physical concepts and is easily to be understood and mastered by engineering designers. Furthermore, this study analyzes the applicability of step-by-step methods including the Newmark beta and Runge-Kutta methods for dynamic response calculation of defective systems. Finally, the implementation procedure of the proposed hybrid approach is illustrated by analyzing numerical examples, and the correctness and the effectiveness of the formula are judged by comparing the results obtained from the different methods. | ||
| Key Words | ||
| damped system; repeated eigenvalues; transfer function; residue matrix; modal superposition method; defective system | ||
| Address | ||
| Rui-fang Yu: Institute of Geophysics, China Earthquake Administration, Beijing, P.R. China Xi-yuan Zhou: Beijing University of Technology, Beijing, P.R. China Mei-qiao Yuan: Institute of Earthquake Engineering, Chongqing, P.R. China | ||