Progress in Structural Dynamics With Stochastic Parameter Variations: 1987-1998

Abstract

This article is an update of an earlier paper by Ibrahim (1987) and is aimed at reviewing the work published during the last decade in the area of vibration of structures with parameter uncertainties. Different types of uncertainty modeling are described in terms of material and geometric properties. These models are considered in terms of Gaussian or non-Gaussian distributions. Computational stochastic algorithms including stochastic finite element methods and Monte Carlo simulation are dominating a major part of current activities. Recent analytical developments of the random eigenvalue problem are reviewed with reference to typical structural elements. These developments include the implementation of statistical energy analysis, stochastic boundary element methods, and interval algebra. Other topics include forced vibration of single-and multi-degree-offreedom systems including nonlinear systems, localization in disordered periodic structures, and experimental results. Computational stochastic mechanics has found several industrial applications including aerospace, automotive and composite structural elements. The review also covers developments in the areas of statistical modeling of high frequency vibrations. There are 183 references.

Stochastic finite element analysis of the free vibration of laminated composite plates

“…These random variables are usually chosen as the composite laminate mechanical properties, density, and orientation angles. Ibrahim [2] and Manohar and Ibrahim [3] has presented a review of structural dynamics problems with such stochastic parameter variations. Oh and Librescu [4] developed a meancentered second-moment method to study the free vibration and reliability of composite cantilevers.…”

Simple Questions for Interactive Information Retrieval

“…The present work is motivated by some recent results on the sensitivity and variability of the response of structural stochasticity (see, for example, Manohar andIbrahim, 1999) and by the recent assessment of joint uncertainties by . These problems are complex in nature because every joint involves different sources of uncertainty and non-smooth nonlinear characteristics.…”

3-D stochastic finite elements for thermal creep analysis of piping structures with spatial material inhomogeneities

“…This constitutes the basis of the subject of stochastic finite element method (SFEM). Discussions and literature review on the various methods of random field discretization and weak form representations are available in [2][3][4][5][6][7][8][9]. An important issue in most SFEM studies is that the random field descriptions are limited to second-order characteristics.…”