Dynamic interaction of plates in an inhomogeneous transversely isotropic space weakened by a crack

A. Amiri-Hezaveh, H. Moghaddasi, P. Karimi, M. Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review


The problem of axisymmetric vibration of a flat thin rigid circular plate located inside a vertically exponentially graded, transversely isotropic material of infinite extent is addressed by means of a displacement potential method. The contact condition on one side of the foundation is assumed to be the perfect adhesion with the media but known to be faced by a penny-shaped crack at the other side as it occurs in anchors. The mixed boundary value problem is formulated with the aid of Hankel integral transforms and is written in the form of a set of singular integral equations. The analytical procedure for the special case of vertical movement of the rigid plate results in a closed form solution. The solution is pursued numerically for the general elastodynamic case. The physical quantities, such as contact stress on the plate and the stress and displacement fields in the non-homogeneous medium are obtained for different materials.

Original languageEnglish (US)
Pages (from-to)1338-1357
Number of pages20
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Issue number11
StatePublished - Nov 2017


  • Exponentially graded material
  • penny-shaped crack
  • rigid plate
  • transversely isotropic space
  • wave propagation

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics

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