Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts

Bhat, Srivatsa K and Ganguli, Ranjan (2018) Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts. In: ROYAL SOCIETY OPEN SCIENCE, 5 (2).

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Abstract

In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam. The boundary-condition configuration should be preserved under this transformation. We present the constraints under which the boundary configurations will remain unchanged. Frequency equivalence of the non-uniform beams and the uniform beam is confirmed by the finite-element method. For the considered cases, examples of beams having a rectangular cross section are presented to show the application of our analysis.

Item Type:	Journal Article
Publication:	ROYAL SOCIETY OPEN SCIENCE
Publisher:	ROYAL SOC, 6-9 CARLTON HOUSE TERRACE, LONDON SW1Y 5AG, ENGLAND
Additional Information:	Copy right for the article belong toROYAL SOC, 6-9 CARLTON HOUSE TERRACE, LONDON SW1Y 5AG, ENGLAND
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	03 Apr 2018 18:27
Last Modified:	03 Apr 2018 18:27
URI:	http://eprints.iisc.ac.in/id/eprint/59464

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