Exploring isospectral spring-mass systems with firefly algorithm

Dutta, Rajdeep and Ganguli, Ranjan and Mani, V (2011) Exploring isospectral spring-mass systems with firefly algorithm. In: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, 467 (2135). pp. 3222-3240.

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Abstract

This paper investigates in-line spring-mass systems (An), fixed at one end and free at the other, with n-degrees of freedom (d.f.). The objective is to find feasible in-line systems (B(n)) that are isospectral to a given system. The spring-mass systems, A(n) and B(n), are represented by Jacobi matrices. An error function is developed with the help of the Jacobi matrices A(n) and B(n). The problem of finding the isospectral systems is posed as an optimization problem with the aim of minimizing the error function. The approach for creating isospectral systems uses the fact that the trace of two isospectral Jacobi matrices A(n) and B(n) should be identical. A modification is made to the diagonal elements of the given Jacobi matrix (A(n)), to create the isospectral systems. The optimization problem is solved using the firefly algorithm augmented by a local search procedure. Numerical results are obtained and resulting isospectral systems are shown for 4 d.f. and 10 d.f. systems.

Item Type:	Journal Article
Publication:	Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
Publisher:	The Royal Society
Additional Information:	Copyright of this article belongs to The Royal Society.
Keywords:	isospectral systems;optimization;vibration;Jacobi matrix
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	25 Oct 2011 10:09
Last Modified:	25 Oct 2011 10:09
URI:	http://eprints.iisc.ac.in/id/eprint/41400

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