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Closed-form solutions for non-uniform Euler-Bernoulli free-free beams

Sarkar, Korak and Ganguli, Ranjan (2013) Closed-form solutions for non-uniform Euler-Bernoulli free-free beams. In: Journal of Sound and Vibration, 332 (23). pp. 6078-6092.

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Official URL: http://dx.doi.org/10.1016/j.jsv.2013.06.008

Abstract

In this paper, the free vibration of a non-uniform free-free Euler-Bernoulli beam is studied using an inverse problem approach. It is found that the fourth-order governing differential equation for such beams possess a fundamental closed-form solution for certain polynomial variations of the mass and stiffness. An infinite number of non-uniform free-free beams exist, with different mass and stiffness variations, but sharing the same fundamental frequency. A detailed study is conducted for linear, quadratic and cubic variations of mass, and on how to pre-select the internal nodes such that the closed-form solutions exist for the three cases. A special case is also considered where, at the internal nodes, external elastic constraints are present. The derived results are provided as benchmark solutions for the validation of non-uniform free-free beam numerical codes. (C) 2013 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
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Additional Information: Copyright of this article belongs to Elsevier Science.
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)
Date Deposited: 29 Oct 2013 05:37
Last Modified: 29 Oct 2013 05:37
URI: http://eprints.iisc.ernet.in/id/eprint/47467

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