Free Vibration Analysis of Moderately Thick Orthotropic Functionally Graded Plates with General Boundary Restraints.

In this paper, a modified Fourier series method is presented for the free vibration of moderately thick orthotropic functionally graded plates with general boundary restraints based on the first-order shear deformation theory. Regardless of boundary restraints, displacements and rotations of each plate are described as an improved form of double Fourier cosine series and several closed-form auxiliary functions to eliminate all the boundary discontinuities and jumps. Exact solutions are obtained by the energy functions of the plates based on Rayleigh-Ritz method. The convergence and reliability of the current method and the corresponding theoretical formulations are verified by comparing the present results with those available in the literature, and numerous new results for orthotropic functionally graded (OFG) plates with general boundary restraints are presented. In addition, the effects of gradient index, volume fraction and geometric parameters on frequencies with general boundary restraints are illustrated.