The stochastic method of weighted residuals for predicting dynamic response of random structure under stochastic excitation
✍ Scribed by Lei, Zhao ;Qiu, Chen
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 157 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1069-8299
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✦ Synopsis
The paper develops a new stochastic weighted-residual method for predicting the dynamic response of a random structure under random excitation. This is achieved by employing a discretization technique in the time domain based on the method of weighted residuals. A trial function involving a third-order B-spline basis function is applied to a replacement of time integration of stochastic ®nite element dynamic equations of the structure. Ecient analysis techniques for the mean values and the variances of the dynamic response are described in detail. Numerical solution results of examples indicate that the approach presented herein eects an economical and ecient solution for such an analysis when compared with Monte Carlo simulation. # 1998 John Wiley & Sons, Ltd. KEY WORDS random structure; stochastic method of weighted residual; dynamic response; spline function
1. Introduction
Traditionally, uncertainty analysis in structural dynamics has concentrated on problems of random vibration. Within this setting, even the mean values and the variances of some simple structures with stochastic parameters under random dynamic loads have not been solved satisfactorily. The most commonly employed solution technique is Monte Carlo simulation (MCS). In general, these simulation procedures are computationally repetitive and therefore expensive, even though they are easily applicable to linear and non-linear random structures. For simple and/or complex random structures in engineering, the perturbation stochastic ®nite element method (PSFEM) based on the second-order perturbation technique is available to the dynamic analysis of structures with random parameters. 1±4 The discretization of three ®elds is included in the dynamic analysis of random structures. The discretization of the spatial displacement ®eld and the random ®eld may be achieved by employing PSFEM. The mean values and the variances of the dynamic response are obtained with the aid of the discretization of the time