Ritz Solutions of Stationary Random Vibrations for GPL-Reinforced FG Rectangular Plate

Abstract

This paper aims to establish a comprehensive model for evaluating the response characteristics of functionally graded graphene platelet-reinforced composite (FG-GPLRC) rectangular plates under stationary random acceleration excitation. Utilizing the first-order shear deformation theory (FSDT) and Halpin–Tsai assumptions, a dynamic model for the rectangular plate is derived, followed by obtaining the variational solution using the Rayleigh–Ritz method. To describe displacement components associated with dynamic equations and boundary conditions, a spectral geometry method (SGM) is employed. Additionally, a pseudo-excitation method (PEM) is utilized for the analysis of stationary random vibration. The proposed calculation method is validated through convergence analysis and comparative evaluation with existing literature and finite element models. Furthermore, the study investigates the influence of various factors, such as boundary conditions, the number and size of functionally graded rectangular plate layers, GPL distribution types, and material parameters, on the stationary random response attributes of FG rectangular plates. This research contributes to a deeper understanding of the dynamic response of functionally graded materials in structural configurations and offers a valuable analytical approach for researchers in this field.