Vibration analysis of functionally graded annular sectorial plates with simply supported radial edges

Assuming that the mechanical properties of the materials vary continuously along the thickness direction and have the same exponential distribution, the free and forced vibration of functionally graded annular sectorial plates with simply supported radial edges and arbitrary circular edges is studied in this paper using a semi-analytical approach (SSM-DQM). The new SSM-DQM method can give an analytical solution along the graded direction using the state space method (SSM) and an effective approximate solution along the radial direction using the one-dimensional differential quadrature method (DQM). The accuracy and convergence of the presented method are demonstrated through numerical examples. For free vibration problems, the influences of various thickness ratios, radii ratios, sector angles, the material property graded indexes and circumferential wave numbers on the lowest non-dimensional frequency are investigated under different circular boundary conditions. And for forced vibration problems, the dynamic response of functionally graded annular sectorial plates under different forcing frequency is studied.