Free vibration of FGM annular sectorial plates with arbitrary boundary supports and large sector angles

Abstract

An original work is presented for the free vibration analysis of thin functionally graded material (FGM) annular sectorial plates with arbitrary boundary supports using the weak form quadrature element method (QEM). Novel C 1 quadrature annular sectorial plate element is developed based on the physically neutral surface thin plate theory in cylindrical coordinate system. Three displacement functions are used to avoid the introduction of the mixed second order derivative degree of freedom at corner points. The derived explicit formulations with a varying node number can be applied for any type of node. A way to define the elastic spring constants is proposed to ensure the independent of the non-dimensional frequency parameter on the power-law exponent. The convergence and accuracy of the present model are validated by comparing the obtained results with those available in literatures. It is demonstrated that the proposed model is simple, straightforward and has good performance. A wide range of numerical results are reported to demonstrate the effect of the sector angle, ratio of inner/outer radii, and boundary conditions on the vibration behavior of the thin annular sectorial plate. Some tabulated results should be new which may serve as a reference for verifying numerical solutions obtained by other methods.