Free vibration of symmetric angle-ply laminated annular circular plate of variable thickness under shear deformation theory

Free vibrational study of symmetric angle-ply laminated annular circular plate of variable thickness including first order shear deformation theory using spline function approximation is studied. The equations of motion for the plates are derived using first order shear deformation theory. The solutions of displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms displacement and rotational functions and these functions are approximated by Bickley-type splines of order three. The vibration of 3- and 5-layered plates, made up of two types of materials and two types of boundary conditions are considered. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. Parametric studies are made of the variation of frequency parameter with respect to the radii ratio, circumferential node number, different sequence, number of lay-ups and other parameters characterizing the nature of variation of thickness for 3- and 5-layers.