Random matrix eigenvalue problems in structural dynamics: An iterative approach

Adhikari, S. and Chakraborty, S. (2022) Random matrix eigenvalue problems in structural dynamics: An iterative approach. Mechanical Systems and Signal Processing, 164, 108260. (doi: 10.1016/j.ymssp.2021.108260)

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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.

Item Type:Articles
Additional Information:SA gratefully acknowledge the support of the Engineering and Physical Sciences Research Council, UK through the award of a program grant, ‘Digital Twins for Improved Dynamic Design’, Grant No. EP/R006768.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Adhikari, Professor Sondipon
Authors: Adhikari, S., and Chakraborty, S.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Mechanical Systems and Signal Processing
Publisher:Elsevier BV
ISSN:0888-3270
ISSN (Online):1096-1216
Published Online:05 August 2021

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