Semi-Analytical Modeling and Vibration Characteristics Analysis of Functionally Graded Material Plates on Winkler-Pasternak Elastic Foundations
Abstract
This study develops a semi-analytical formulation for analyzing the dynamic behaviors of functionally graded plates resting on Winkler-Pasternak elastic foundations. To begin with, the energy formulations for the plate structure are established through incorporating the domain decomposition approach, the first-order shear deformation theory and artificial spring method. Kinematic admissible functions are constructed by the superposition of orthogonal Jacobi polynomials, and the functionally graded materials exhibit continuous property variation along the thickness direction is mathematically defined. Subsequent implementation of the Rayleigh-Ritz variational principle enables systematic resolution of free and forced vibrational behaviors, and the Newmark-β integration approach is used to solve the time domain vibration response of the structure, while validation studies demonstrate exceptional consistency with benchmark solutions from the existing literatures. Ultimately, the influence of the characteristic parameters such as boundary conditions, construction parameters, foundation parameters, and power-law distribution on the dynamic behavior is carried out.