Free vibration of laminated cross-ply plates with variable thickness including shear deformation theory

Abstract

Free vibration of laminated cross-ply plates of variable thickness including transverse shear deformation are studied using spline approximation. The method of collocation with splines is applied due to the possibility that a chain of lower order approximations can yield greater accuracy than a global high order approximation. By assuming the solution in a separable form to attain a system of coupled differential equations in displacement and rotational functions than these functions are approximated using Bickley-type splines of order three. A generalized eigenvalue problem is solved numerically to obtain eigenvalues as frequency parameter and an associated eigenvectors are spline coefficients. Parametric studies have to be done to analyze the variation of frequency parameters with respect to the aspect ratio, side-to- thickness ratio ply-angle, number of layer and thickness variations.