Dynamic Analysis of Functionally Graded L-Shaped Plates with General Boundary Conditions

The dynamic model of functionally graded coupled L-shaped plates is established by a semi-analytical method in this study. To begin with, the energy expressions of the plate are derived by incorporating the domain decomposition approach, artificial spring method and shear deformation plate theory. Kinematic admissible functions are constructed via superposition of characteristic orthogonal Jacobi polynomials. The through-thickness direction of functionally graded material is governed by a generalized four parameter power-law model, which enables precise control of continuous material property gradation across transverse cross-sections. Subsequent implementation of the Rayleigh-Ritz variational principle enables systematic resolution of free and forced vibrational behaviors, and the Newmark-β integration method is used to the time domain analysis, while validation studies demonstrate exceptional consistency with benchmark solutions from both existing literature and Finite Element Method (FEM) simulations. Ultimately, the influence of the characteristic parameters such as boundary restraints, dispersion patterns, construction parameters, and power-law distribution on the dynamic behavior is carried out.