Free vibration analysis of thin circular and annular plate with general boundary conditions

Abstract

This paper presents a numerical analysis of free vibration of thin circular and annular plate using finite element method. The first five natural frequencies are presented for uniform annular plates of various inner-to-outer radius ratios, with nine possible combinations of free, clamped and simply supported boundary conditions at the inner and outer edges of plates. The accuracy of the method is established by comparing the results available in the literature. Results show that natural frequency parameter increases as the inner-to-outer radius ratio increases except in case of free boundary condition, for which it decreases with the inner-to-outer radius ratio. This result provides benchmark values that can be used to validate result obtained by other approximate approaches such as finite difference method, differential quadrature method and boundary element method.