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Random matrix eigenvalue problems in structural dynamics: An iterative approach / Sondipon Adhikari, S. Chakraborty

Mechanical Systems and Signal Processing, Volume: 164, Start page: 108260

Swansea University Author: Sondipon Adhikari

  • Accepted Manuscript under embargo until: 5th August 2022

Abstract

Uncertainties need to be taken into account in the dynamic analysis of complex structures. This is because in some cases uncertainties can have a significant impact on the dynamic response and ignoring it can lead to unsafe design. For complex systems with uncertainties, the dynamic response is char...

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Published in: Mechanical Systems and Signal Processing
ISSN: 0888-3270
Published: Elsevier BV 2022
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa57554
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Abstract: Uncertainties need to be taken into account in the dynamic analysis of complex structures. This is because in some cases uncertainties can have a significant impact on the dynamic response and ignoring it can lead to unsafe design. For complex systems with uncertainties, the dynamic response is characterised by the eigenvalues and eigenvectors of the underlying generalised matrix eigenvalue problem. This paper aims at developing computationally efficient methods for random eigenvalue problems arising in the dynamics of multi-degree-of-freedom systems. There are efficient methods available in the literature for obtaining eigenvalues of random dynamical systems. However, the computation of eigenvectors remains challenging due to the presence of a large number of random variables within a single eigenvector. To address this problem, we project the random eigenvectors on the basis spanned by the underlying deterministic eigenvectors and apply a Galerkin formulation to obtain the unknown coefficients. The overall approach is simplified using an iterative technique. Two numerical examples are provided to illustrate the proposed method. Full-scale Monte Carlo simulations are used to validate the new results.
Keywords: Random eigenvalue problem, Iterative methods, Galerkin projection, Statistical distributions, Stochastic systems
College: College of Engineering
Start Page: 108260