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Shock and Vibration
Volume 11 (2004), Issue 5-6, Pages 615-624

Non-Stationary Random Response of MDOF Duffing Systems

J.H. Lin,1 J. Wang,2 and Y.H. Zhang1

1State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China
2Department of Civil Engineering, SUNY at Buffalo, 109 Red Jacket Quard., Buffalo, NY 14261, USA

Received 16 December 2003; Revised 16 March 2004

Copyright © 2004 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.


This paper presents a method to solve non-stationary random responses of nonlinear multi-degrees-of-freedom (MDOF) Duffing systems subjected to evolutionary random excitations. Specific phase-lags between the excitations can also be taken into account. The power spectral density (PSD) of the input excitations is not confined to simple white noise or filtered white noise, in fact it can also take more complicated forms. The MDOF nonlinear random differential equations are iteratively solved by means of the Equivalent Linearization Method (ELM) combined with the Pseudo Excitation Method (PEM). This combined method is easy and efficient. Two examples are given in which this method is well justified by the Monte-Carlo numerical simulations. Although only a Duffing model is dealt with in this paper for computational simplicity, the proposed method is in fact quite general, e.g. it can also deal with nonlinear hysteretic structures that will be dealt with in a separate paper.