Free vibration analysis of functionally graded rectangular plates under asymmetric boundary conditions using coupled displacement field method

Purpose The purpose of this paper is to investigate the free vibration behavior of a functionally graded (FG) rectangular plate under asymmetric boundary conditions using the coupled displacement field method (CDF), which is based on first-order shear deformation theory (FSDT). Design/methodology/approach The material properties of the FG rectangular plate vary continuously in the direction of thickness based on the power-law exponent form. The approach utilizes the CDF method, where the admissible trail functions are assumed for total rotations in both directions that satisfy various boundary conditions. Based on the coupling equations, the function for lateral displacement is derived in terms of total rotations. By utilizing the energy formulations, the undetermined coefficients are derived. The frequency parameters are obtained by minimizing the Lagrangian with respect to the undetermined coefficients. Findings The frequencies with respect to different parameters like aspect ratios ( a/b ), thickness ratio ( h/a ) and power-law ( k ) for all edges SCSS and SCSF boundary conditions are found. The effect of the parameters on the obtained frequencies is observed, and these frequency parameters are compared with other literature to validate the derived frequencies. The findings of the present formulation are in excellent accord when compared to other methods in the literature. Originality/value The energy formulations in the proposed method contain half the number of undetermined coefficients when compared to the Rayleigh–Ritz (RR) method, which simplifies the vibration problem significantly. The efficacy of the proposed method in finding the frequency parameters lies in reduced computational procedure when compared to other methods.