Chinese Journal of Theoretical and Applied Mechani ›› 2007, Vol. 23 ›› Issue (1): 112-118.DOI: 10.6052/0459-1879-2007-1-2006-170

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Modal perturbation method for obtaining complex modal characteristics of non-proportional damping systems

Menglin Lou Yaoqing Fan   

  • Received:2006-04-17 Revised:2006-09-05 Online:2007-01-18 Published:2007-01-18

Abstract: An approximate approach based on the direct modal perturbation method is suggested for analyzing the complex modal characteristics of non-proportional damping structure systems. The proposed approach uses the expansion of complex Ritz vectors. The procedure is in two steps. First, the subspace of the solution based on the complex vectors is formed by using the conventional real modes of the structure. Then, a set of solutions of non-linear complex algebraic equations is established to displace the solution of the complex eigen-value equations. The results of two numerical examples show that the suggested method simplifies the solving procedure and is of high precision and efficiency. It can be used for the solution of the complex modal characteristics and dynamic responses of non-proportional damping structure systems.

Key words: non-proportionally damping, complex modal characteristics, modal perturbation method, expansion of complex Ritz vectors, complicated structure