A hybrid energy approach for vibrational modelling of laminated trapezoidal plates with point supports

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Original languageEnglish
Pages (from-to)3087-3097
Journal / PublicationInternational Journal of Solids and Structures
Issue number24
Publication statusPublished - 1992
Externally publishedYes


An investigation on the free flexural vibration of symmetric angle-ply thin trapezoidal plates continuous over arbitrarily distributed point supports is reported. A hybrid energy approach which combines the pb-2 Rayleigh-Ritz method with the Lagrangian multiplier method is proposed for the modelling of the aforementioned plate problem. The pb-2 Rayleigh-Ritz method uses a set of Ritz functions generated from the product of a two-dimensional polynomial and the equations of boundaries each raised to the power of 0, 1 or 2 corresponding to a free, simply-supported or clamped edge, respectively. The geometric boundary conditions associated with the point supports are satisfied through the use of Lagrangian multipliers. In this paper, some new solutions for the natural frequencies of several laminated trapezoidal plates with different stacking sequences and location of point supports are presented. The first known mode shapes by means of contour plots for such laminated plates are also included. © 1992.