Stiff string approximations in Rayleigh-Ritz method for rotating beams

Ganesh R, Ranjan Ganguli

Research output: Contribution to journalArticle

26 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)9282-9295
Number of pages14
JournalApplied Mathematics and Computation
Volume219
Issue number17
DOIs
StatePublished - Apr 29 2013

Keywords

  • Gram-Schmidt orthogonalization
  • Rayleigh's quotient
  • Rayleigh-Ritz
  • Rotating beams
  • Stiff string function

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