Free in-plane vibration analysis of elastically restrained annular panels made of functionally graded material

In this paper, free in-plane vibration of elastically restrained annular plate made of functionally gradient material (FGM) is investigated by an improved Fourier series method. The material property is assumed to be gradually changed in power law along the radial direction. The energy equation is formulated for the in-plane free vibration description of FGM annular plate, with the admissible functions constructed as the superposition of standard Fourier series and boundary smoothed polynomials to make the spatial differential continuous enough in the entire solving domain. In conjunction with the Rayleigh-Ritz procedure, system characteristic equation in matrix form is straightforwardly derived. Several numerical examples are then presented to validate the proposed model, and study the in-plane vibration characteristics of FGM annular panel with various boundary conditions. Based on the model established, the influence of important parameters, such as FGM power-law exponent and boundary restraints, on the in-plane vibration characteristics of FGM annular panel is addressed and investigated in detail. This work can shed some light for a better understanding on the in-plane dynamic characteristics of such complex structure.