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Rotating Beams and Nonrotating Beams With Shared Eigenpair

Kumar, Ananth and Ganguli, Ranjan (2009) Rotating Beams and Nonrotating Beams With Shared Eigenpair. In: Journal of Applied Mechanics, 76 (5). pp. 1-14.

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Abstract

In this paper, we look for rotating beams whose eigenpair (frequency and mode-shape) is the same as that of uniform nonrotating beams for a particular mode. It is found that, for any given mode, there exist flexural stiffness functions (FSFs) for which the jth mode eigenpair of a rotating beam, with uniform mass distribution, is identical to that of a corresponding nonrotating uniform beam with the same length and mass distribution. By putting the derived FSF in the finite element analysis of a rotating cantilever beam, the frequencies and mode-shapes of a nonrotating cantilever beam are obtained. For the first mode, a physically feasible equivalent rotating beam exists, but for higher modes, the flexural stiffness has internal singularities. Strategies for addressing the singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to The American Society of Mechanical Engineers.
Keywords: Free-vibration analysis;dynamic stiffness method;euler-bernoulli beams;finite-element method; uniform;blades; singularities.
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)
Date Deposited: 04 Jan 2010 11:05
Last Modified: 19 Sep 2010 05:37
URI: http://eprints.iisc.ernet.in/id/eprint/21336

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