Viswanathan K.

Abstract The free vibration of layered annular circular plate of variable thickness, made up of isotropic or specially orthotropic materials, is studied using spline function approximation by applying the point collocation method. Three different thickness variations are considered, namely, linear, exponential and sinusoidal, along the radial directions. The equations of motion are derived by extending Love’s first approximation theory. A system of coupled differential equations, in the longitudinal, circumferential and transverse displacement functions is obtained by assuming the solution in a separable form. These functions are approximated by using Bickley-type splines of suitable orders. A generalized eigenvalue problem is obtained by applying a point collocation technique and suitable boundary conditions from which the values of a frequency parameter and the corresponding mode shapes of vibration, for specific values of other parameters, are obtained.