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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
 


Dynamic response analysis of generally damped linear system with repeated eigenvalues
Rui-fang Yu, Xi-yuan Zhou and Mei-qiao Yuan

 
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
 

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