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Shock and Vibration
Volume 7, Issue 4, Pages 209-216

High Efficiency Computation of the Variances of Structural Evolutionary Random Responses

J.H. Lin,1 D.K. Sun,2 W.X. Zhong,1 and W.S. Zhang2

1State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China
2Dept of Civil and Structural Engineering, Hong Kong Polytechnic University, Kowloon, Hung Hom, Hong Kong

Received 23 April 1999; Revised 14 April 2000

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For structures subjected to stationary or evolutionary white/colored random noise, their various response variances satisfy algebraic or differential Lyapunov equations. The solution of these Lyapunov equations used to be very difficult. A precise integration method is proposed in the present paper, which solves such Lyapunov equations accurately and very efficiently.