Wavelet-based method for stability analysis of vibration control systems with multiple delays

Authors:
Jun Zhou;You-He Zhou;K. M. Liew
Affiliations:
Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong and Key Laboratory of Mechanics on Western Disaster and Environment, Lanzhou University, Lanzhou, People's ...;Key Laboratory of Mechanics on Western Disaster and Environment, Lanzhou University, Lanzhou, People's Republic of China 730000;Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong
Venue:
Computational Mechanics
Year:
2011

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Abstract

A new method based on wavelets is proposed for stability analysis of vibration control system with multiple delays. In this method, solutions of the initial-value problem of time delayed vibration control systems are approximated by wavelets. Applying wavelet collocation method, the initial-value problem of the time delayed vibration control systems is transformed to a mapping system. The stability of the original system depends on the maximal modulus of eigenvalues of the mapping matrix, and the numerical solution of the initial-value problem are obtained by solving the mapping system. Numerical examples show that the method can locate stable and unstable regions in parameter planes and produces accurate numerical solutions of initial-value problems of time delayed systems.