Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

Ghosh, Debraj (2013) Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure. In: Archive of Applied Mechanics, 83 (9). pp. 1341-1357.

PDF Arch_Appl_Mech_83-9_1341_2013.pdf - Published Version Restricted to Registered users only Download (1MB) | Request a copy

Abstract

The random eigenvalue problem arises in frequency and mode shape determination for a linear system with uncertainties in structural properties. Among several methods of characterizing this random eigenvalue problem, one computationally fast method that gives good accuracy is a weak formulation using polynomial chaos expansion (PCE). In this method, the eigenvalues and eigenvectors are expanded in PCE, and the residual is minimized by a Galerkin projection. The goals of the current work are (i) to implement this PCE-characterized random eigenvalue problem in the dynamic response calculation under random loading and (ii) to explore the computational advantages and challenges. In the proposed method, the response quantities are also expressed in PCE followed by a Galerkin projection. A numerical comparison with a perturbation method and the Monte Carlo simulation shows that when the loading has a random amplitude but deterministic frequency content, the proposed method gives more accurate results than a first-order perturbation method and a comparable accuracy as the Monte Carlo simulation in a lower computational time. However, as the frequency content of the loading becomes random, or for general random process loadings, the method loses its accuracy and computational efficiency. Issues in implementation, limitations, and further challenges are also addressed.

Item Type:	Journal Article
Publication:	Archive of Applied Mechanics
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Keywords:	Random Eigenvalue; Stochastic Dynamics; Structural Dynamics; Probabilistic Mechanics
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	24 Sep 2013 06:25
Last Modified:	24 Sep 2013 06:25
URI:	http://eprints.iisc.ac.in/id/eprint/47421

Actions (login required)

View Item