Free vibration of anti-symmetric angle-ply plates with variable thickness

Abstract

Free vibration of anti-symmetric angle-ply plates with variable thickness is analysed using spline function approximation including the effect of shear deformation. The equations of motion for the plate are derived using the theory of Yang, Norris and Stavsky. Assuming the solution in a separable form, a system of coupled differential equations in displacement and rotational functions are obtained and these functions are approximated by Bickley-type splines of order three. A generalised eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. Two and four layered plates consisting of two different materials and plies comprising of same as well as different materials for two different boundary conditions are analysed. The effect of material properties, ply orientation, number of lay ups, aspect ratio and coefficients of thickness variations on the frequency parameter are presented. The accuracy of the result is ascertained by convergence and comparative study.