Vibrations of rectangular plates with internal cracks or slits

Chiung-Shiann Huang, A. W. Leissa, C. W. Chan

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


This work applies the famous Ritz method to analyze the free vibrations of rectangular plates with internal cracks or slits. To retain the important and useful feature of the Ritz method providing the upper bounds on exact natural frequencies, the paper proposes a new set of admissible functions that are able to properly describe the stress singularity behaviors near the tips of the crack and meet the discontinuous behaviors of the exact solutions across the crack. The validity of the proposed set of functions is confirmed through comprehensive convergence studies on the frequencies of simply supported square plates with horizontal center cracks having different lengths. The convergent frequencies show excellent agreement with published accurate results obtained by an integration equation technique, and are more accurate than those obtained by a previously published approach using the Ritz method combined with a domain decomposition technique. Finally, the present solution is employed to obtain accurate natural frequencies and mode shapes for simply supported and completely free square plates with internal cracks having various locations, lengths, and angular orientations. Most of the configurations considered here have not been analyzed in the previously published literature. The present results are novel, and are the first published vibration data for completely free rectangular plates with internal cracks and for plates with internal cracks, which are not parallel to the boundaries.

Original languageEnglish
Pages (from-to)436-445
Number of pages10
JournalInternational Journal of Mechanical Sciences
Issue number6
StatePublished - 1 Jun 2011


  • Cracked plates
  • Ritz method
  • Special admissible functions
  • Vibrations


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