Vibration of circular and annular plates using finite elements

Abstract

Abstract The finite element method is applied to the free transverse vibration of circular and annular plates of varying thickness. An annular element is derived which incorporates the number of diametral modes in the deflection function. This results in an element having only four degrees of freedom, these being the deflection and slopes at the inner and outer radii of the element at an anti‐node of the particular vibration mode. Thickness variation in the radial direction is readily introduced, and stiffness and inertia matrices are presented for elements with linear and parabolic variations in thickness. The method is checked with several numerical examples. Calculations of free vibration of circular and annular plates of constant, linear and parabolic thickness variation are compared with available exact solutions.