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Stiff string approximations in Rayleigh-Ritz method for rotating beams

Ganesh, R and Ganguli, Ranjan (2013) Stiff string approximations in Rayleigh-Ritz method for rotating beams. In: Applied Mathematics and Computation, 219 (17). pp. 9282-9295.

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Official URL: http://dx.doi.org/10.1016/j.amc.2013.03.017


The governing differential equation of the rotating beam reduces to that of a stiff string when the centrifugal force is assumed as constant. The solution of the static homogeneous part of this equation is enhanced with a polynomial term and used in the Rayleighs method. Numerical experiments show better agreement with converged finite element solutions compared to polynomials. Using this as an estimate for the first mode shape, higher mode shape approximations are obtained using Gram-Schmidt orthogonalization. Estimates for the first five natural frequencies of uniform and tapered beams are obtained accurately using a very low order Rayleigh-Ritz approximation.

Item Type: Journal Article
Publication: Applied Mathematics and Computation
Publisher: Elsevier Science
Additional Information: Copyright of this article belongs to Elsevier Science.
Keywords: Rotating Beams; Stiff String Function; Rayleigh's Quotient; Rayleigh-Ritz; Gram-Schmidt Orthogonalization
Department/Centre: Division of Interdisciplinary Sciences > Supercomputer Education & Research Centre
Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 21 Jun 2013 05:12
Last Modified: 21 Jun 2013 05:12
URI: http://eprints.iisc.ac.in/id/eprint/46721

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