Effects of damaged boundaries on the free vibration of kirchhoff plates: Comparison of perturbation and spectral collocation solutions

Ma'en Sari, Morad Nazari, Eric A. Butcher

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

In order to compare numerical and analytical results for the free vibration analysis of Kirchhoff plates with both partially and completely damaged boundaries, the Chebyshev collocation and perturbation methods are utilized in this paper, where the damaged boundaries are represented by distributed translational and torsional springs. In the Chebyshev collocation method, the convergence studies are performed to determine the sufficient number of the grid points used. In the perturbation method, the small perturbation parameter is defined in terms of the damage parameter of the plate, and a sequence of recurrent linear boundary value problems is obtained which is further solved by the separation of variables technique. The results of the two methods are in good agreement for small values of the damage parameter as well as with the results in the literature for the undamaged case. The case of mixed damaged boundary conditions is also treated by the Chebyshev collocation method.

Original languageEnglish (US)
Article number011011
JournalJournal of Computational and Nonlinear Dynamics
Volume7
Issue number1
DOIs
StatePublished - Jan 2012

Keywords

  • Chebyshev collocation
  • Damaged boundary
  • Free vibration analysis
  • Perturbation method
  • Rectangular plate

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics

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