Free vibration of a mindlin annular plate of varying thickness

Abstract

The free vibration of a Mindlin annular plate of radially varying thickness is analyzed by use of the transfer matrix approach. For this purpose, the Mindlin equations of flexural vibration of an annular plate are written as a coupled set of first-order differential equations by using the transfer matrix of the plate. Once the matrix has been determined by the numerical integration of the equations, the natural frequencies and the mode shapes of the vibration are calculated numerically in terms of the elements of the matrix for a given set of boundary conditions at the edges of the plate. This method is applied to annular plates of linearly, parabolically and exponentially varying thickness, and the effects of the varying thickness are studied.