Free Vibration Analysis of Simply Supported and Clamped Functionally Graded Rectangular Plate Using Coupled Displacement Field Method

Abstract

In this paper, a coupled displacement field (CDF) method was proposed to examine the free vibration behavior of a functionally graded (FG) rectangular plate with simply supported (SSSS) and clamped (CCCC) boundary conditions. The composition of the functionally graded rectangular plate is ceramic on the top and metal on the bottom. According to the power-law exponent form, the rectangular plate material properties vary continuously in the thickness direction. The trial functions signifying the displacement constituents of the cross-sections of the plate are stated in simple algebraic polynomial forms. The lateral displacement field is derived in terms of the total rotations with the help of coupling equations. By utilizing the energy formulation, the undetermined coefficients are obtained. The frequency parameters with various aspect ratios, thickness ratios, and power-law for all edges are simply supported and clamped boundary conditions are derived. To validate the numerical results, a comparison of frequency parameters is done with other literature.

Keywords

• aspect ratio
• first-order shear deformation theory
• frequency parameters
• power law
• thickness ratio