Three-dimensional transient analysis of functionally graded material annular sector plate under various boundary conditions

A semi-analytical methodology is developed for the transient response of FGM annular sector plate with arbitrary circular boundary conditions. The state space method, differential quadrature method and the numerical inversion method of Laplace transform are integrated into this methodology. The FGM annular sector plate is simply supported at the radial edges. At the circular edges, four kinds of boundary conditions are considered in this paper: Clamped–Clamped, Clamped–Simply supported, Clamped–Free and Simply supported–Simply supported. A comparison of the results generated by the present and finite element method is carried out. It shows that the results of the present and the finite element method always agree with each other excellently, regardless of which boundary condition, load and geometry are employed. The present method is further validated by comparing the fundamental frequency parameters with those in the literature. Moreover, convergence studies for different numbers of sampling points along the radial direction and layer numbers along the thickness direction are performed. It is found that this methodology has fast convergence rate. The effects of the boundary conditions, the functionally graded index, and the thickness on the plate response are also investigated. The results obtained in this paper can serve as benchmark data in further research.