Free vibration of laminated cross-ply plates including shear deformation by spline method

Spline function approximation technique is used to analyze the free vibration of symmetric and anti-symmetric cross-ply plates under shear deformation theory. The equations of motion of the plate are derived using YNS theory. A system of coupled differential equations in terms of displacement and rotational functions are obtained by assuming the solution in a separable form. These functions are approximated using Bickley-type splines of suitable orders. A generalized eigenvalue problem is obtained on applying the process of point collocation with suitable boundary conditions. Parametric studies have been made to investigate the frequency response of the plates with reference to the material properties, number of layers, fiber orientation, side-to-thickness ratio, aspect ratio and relative layer thickness. Some results are compared with existing solution obtained by FEM.