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Shock and Vibration
Volume 18, Issue 1-2, Pages 387-396

Stochastic Responses of Multi-Degree-of-Freedom Uncertain Hysteretic Systems

Yimin Zhang

School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110004, China

Received 9 February 2010; Revised 2 June 2010

Copyright © 2011 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.


On the basis of the Bouc-Wen hysteretic model, the effective numerical method for the response of nonlinear multi-degree-of-freedom (MDOF) stochastic hysteretic systems is presented using second moment method. Using this method, the mean values, variances and covariances are computed. The Monte Carlo simulation is applied to validate the method. The results obtained by the two methods are contrasted, and the solutions of the method in this paper agreed very well with the Monte Carlo simulation. It has solved the random response of nonlinear stochastic vibration systems which is caused by the stochastic hysteretic loop itself.