Two-Dimensional Elasticity Solutions for In-Plane Free Vibration of FGM Rectangular Plates under Different Boundary Conditions

In order to obtain the dynamic responses on in-plane free vibration of functionally graded material (FGM) rectangular plates, based on the two-dimensional linear elasticity theory, the governing partial differential equations for the in-plane free vibration of FGM rectangular plates were derived. Using differential quadrature method (DQM), the frequency characteristics for in-plane free vibration of FGM rectangular plates under 9 different boundary conditions were investigated. The effects of boundary conditions, geometrical parameters and material gradient indexes on the dimensionless frequencies of the FGM rectangular plates were analyzed. The material gradient index was set as zero to take FGM rectangular plates as isotropic rectangular plates. Then, the applicability and accuracy of the DQM were demonstrated by comparing the in-plane free vibration of the obtained isotropic rectangular plates with those in literature. The effect of the length-width ratio on the fundamental frequency of the FGM rectangular plates varies under different boundary conditions. The fundamental frequency increases with the length-width ratios for the plates C-C-C-C, SS2-C-SS2-C, C-C-C-F, SS1-C-SS1-C, C-C-F-F and SS1-SS1-SS2-SS2, and decreases with the increase of the length-width ratios for the plates F-F-F-F and C-F-C-F, but has no significant changes for SS1-SS1-SS1-SS1 plate because of shear locking. The fundamental frequency decreases rapidly with the increase of material gradient indexes, but it has no obvious change when the material gradient index p is more than 10.