Stability and vibration of shear deformable plates - First order and higher order analyses

I. Shufrin, M. Eisenberger

Research output: Contribution to journalArticlepeer-review

142 Scopus citations


This work presents the highly accurate numerical calculation of the natural frequencies and buckling loads for thick elastic rectangular plates with various combinations of boundary conditions. The Reissener-Mindlin first order shear deformation plate theory and the higher order shear deformation plate theory of Reddy have been applied to the plate's analysis. The governing equations and the boundary conditions are derived using the dynamic version of the principle of minimum of the total energy. The solution is obtained by the extended Kantorovich method. This approach is combined with the exact element method for the vibration and stability analysis of compressed members, which provides for the derivation of the exact dynamic stiffness matrix including the effect of in-plane and inertia forces. The large number of numerical examples demonstrates the applicability and versatility of the present method. The results obtained by both shear deformation theories are compared with those obtained by the classical thin plate's theory and with published results. Many new results are given too.

Original languageEnglish
Pages (from-to)1225-1251
Number of pages27
JournalInternational Journal of Solids and Structures
Issue number3-4
StatePublished - 1 Feb 2005
Externally publishedYes


  • Dynamic stiffness
  • Extended Kantorovich method
  • First order plate theory
  • Higher order plate theory
  • Plate buckling and vibration

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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