Three-dimensional vibration analyses of functionally graded material rectangular plates with through internal cracks

Chiung-Shiann Huang*, P. J. Yang, M. J. Chang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The free vibrations of rectangular FGM plates with through internal cracks are investigated using the Ritz method. Three-dimensional elasticity theory is employed, and new sets of admissible functions for the displacement fields are proposed to enhance the effectiveness of the Ritz method in modeling the behaviors of cracked plates. The proposed admissible functions accurately describe the stress singularities at the fronts of the crack and display displacement discontinuities across the crack. The correctness and validity of the present approach are established through comprehensive convergence studies and comparisons with published results for homogeneous cracked plates, based on various plate theories. The locally effective material properties of FGM in the thickness direction are estimated by a simple power law. The effects of the volume fraction of the constituents of FGM and the thickness-to-length ratio on the frequencies are investigated. Frequency data for FGM square plates with three types of boundary conditions along the four side faces and with internal cracks of various crack lengths, positions and orientations are tabulated for the first time.

Original languageEnglish
Pages (from-to)2764-2776
Number of pages13
JournalComposite Structures
Issue number9
StatePublished - 1 Sep 2012


  • Cracked plate
  • Functionally graded material
  • Ritz method
  • Three-dimensional elasticity theory
  • Vibration


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