Free vibration analysis of rectangular and annular Mindlin plates with undamaged and damaged boundaries by the spectral collocation method

Ma'En S. Sari, Eric Butcher

Research output: Contribution to journalArticle

15 Scopus citations


The objective of this paper is the development of a new numerical technique for the free vibration analysis of isotropic rectangular and annular Mindlin plates with damaged boundaries. For this purpose, the Chebyshev collocation method is applied to obtain the natural frequencies of Mindlin plates with damaged clamped boundary conditions, where the governing equations and boundary conditions are discretized by the presented method and put into matrix vector form. The damaged boundaries are represented by distributed translational and torsional springs. In the present study the boundary conditions are coupled with the governing equation to obtain the eigenvalue problem. Convergence studies are carried out to determine the sufficient number of grid points used. First, the results obtained for the undamaged plates are verified with previous results in the literature. Subsequently, the results obtained for the damaged Mindlin plate indicate the behavior of the natural vibration frequencies with respect to the severity of the damaged boundary. This analysis can lead to an efficient technique for structural health monitoring of structures in which joint or boundary damage plays a significant role in the dynamic characteristics. The results obtained from the Chebychev collocation solutions are seen to be in excellent agreement with those presented in the literature.

Original languageEnglish (US)
Pages (from-to)1722-1736
Number of pages15
JournalJVC/Journal of Vibration and Control
Issue number11
Publication statusPublished - Oct 2012
Externally publishedYes



  • Chebyshev collocation method
  • damaged boundaries
  • eigenvalue problem
  • free vibration
  • rectangular plates

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)
  • Aerospace Engineering
  • Automotive Engineering

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