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Analogy Between Rotating Euler-Bernoulli and Timoshenko Beams and Stiff Strings

Kumar, Vinod AS and Ganguli, Ranjan (2012) Analogy Between Rotating Euler-Bernoulli and Timoshenko Beams and Stiff Strings. In: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 88 (6). pp. 443-474.

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Official URL: http://www.techscience.com/doi/10.3970/cmes.2012.0...


The governing differential equation of a rotating beam becomes the stiff-string equation if we assume uniform tension. We find the tension in the stiff string which yields the same frequency as a rotating cantilever beam with a prescribed rotating speed and identical uniform mass and stiffness. This tension varies for different modes and are found by solving a transcendental equation using bisection method. We also find the location along the rotating beam where equivalent constant tension for the stiff string acts for a given mode. Both Euler-Bernoulli and Timoshenko beams are considered for numerical results. The results provide physical insight into relation between rotating beams and stiff string which are useful for creating basis functions for approximate methods in vibration analysis of rotating beams.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to TECH SCIENCE PRESS, USA
Keywords: Rotating beam;Centrifugal stiffening;Finite element;Bisection method;Frequency;Vibration
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 09 Mar 2013 07:21
Last Modified: 09 Mar 2013 07:21
URI: http://eprints.iisc.ac.in/id/eprint/46010

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