Random structural dynamic response analysis under random excitation

Abstract

Liao JunCollege of Mechanical and Electrical Engineering, Central South University, Changsha, 410001, China e-mail: liaojun@csu.edu.cn Xu DafuAerospace System Engineering Shanghai, Shanghai, 201108, China Jiang BingyanSchool of Aeronautics and Astronautics, Central South University, Changsha, 410001, China IntroductionIn practical engineering problems, not only the external excitations such as wind loading, seismic waves etc., demonstrate uncertainty, but also the structural parameters exhibit uncertainty. The uncertainty of structural parameters may have a strong influence on structural reliability. [1, 2], therefore it is more reasonable to consider the variability of structural physical parameters in dynamic response analysis of structures.The double random vibration analysis, i.e. the random vibration analysis of stochastic parameter structures subjected to random excitation, attracts much interest in researchers. In current literatures there are mainly three ways to tackle this problem. The first is Monte Carlo simulation method [1]. This method is robust and powerful in this aspect of structural analysis, but it is very time-consuming. The second is stochastic finite element method. Although the random eigen value problem, static analysis problem and structural stability problem, etc. can be solved efficiently with this method [2], the stochastic finite method is haunted by the notorious secular term in random dynamic response analysis of structures. The third is orthogonal series expansion method [3][4][5][6] in which the structural response is expanded as a set of orthogonal series and the corresponding numerical characteristics are given as analytical solution. Li [6] developed an order expanded system method by applying sequential orthogonal expansion to deal with double random vibration analysis. Some numerical examples indicate that orthogonal series expansion method avoids the secular term of perturbation methods and does not have to assume the variability of structural parameters to be small. However, the method is still very timeconsuming for large degree of freedom FE model. C.A. Schenk and H.J. Pradlwarter [7][8][9] developed a method to deal with dynamic stochastic response of FE models under non-stationary random excitation, non-zero mean, non-white, non-stationary Gaussian distributed excitation is represented by the well known K-L expansion. For the case where the stochastic loading is described by a finite set of deterministic K-L vectors, which in fact is considered in this paper, and to deal with double random vibration analysis. Then, the classic vibration analysis method can apply to the order-expanded equation, and the probabilistic in-

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