On the Vibration and Buckling of Orthotropic Plates of Variable Thickness

Abstract

<p> The problem of a thin, orthotropic skew plate of linearly varying thickness for vibration and buckling analyses is formulated under the assumptions of small-deflection theory of plates. Using the dimensionless oblique coordinates, the deflection surface of the plate is expressed as a polynomial series, each term of which satisfying the required polar symmetry conditions, and the natural frequencies are computed using Galerkin method. As is required in Galerkin method, the assumed deflection function satisfies all the boundary conditions on all the edges of the plate. For the skew plate, clamped on all the four edges, numerical results for the first few natural frequencies are presented for various combinations of aspect ratio, skew angle and taper parameter. Convergence study has been made for typical configuration of the plate and the limited available data is inserted therein along with the computed results, for comparison.</p>