A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

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Original languageEnglish
Pages (from-to)4937-4954
Journal / PublicationInternational Journal of Solids and Structures
Issue number28-29
Publication statusPublished - 22 May 2001
Externally publishedYes


A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element. Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates. © 2001 Elsevier Science Ltd. All rights reserved.

Research Area(s)

  • Abrupt thickness variation, Free vibration, Plates, Polynomials, Ritz method