Thermal Vibration Analysis of Functionally Graded Porous Plates Reinforced by Graphene Platelets Supported by Arbitrarily Distributed Kerr Foundations Under a Nonlinear Temperature Profile

Functionally graded porous plates reinforced by graphene platelets (FGP-GPLs) have great potential value in areas such as aerospace and high-temperature electronic components. The analysis of vibrational characteristics of FGP-GPLs plates in thermal environments is important for the safety performance and optimization of these structures. However, the current thermal vibration analysis of FGP-GPLs plates does not use the nonlinear temperature profile (NTP), and the case of a plate supported by an arbitrarily distributed elastic foundation is not considered in the vibration analysis of FGP-GPLs plates. The purpose of this paper is to investigate the thermal vibrational characteristics of FGP-GPLs plates supported by arbitrarily distributed elastic foundations under NTP.

First, the shape and location of the three-parameter Kerr foundations are determined by mathematical functions. Four typical foundation distributions pattern are given in the paper. Second, the NTP model is obtained by solving the steady-state heat transfer model. This distribution model considers the effects of pores and GPLs. Third, the control equations of the plate are obtained using Hamilton's principle and refined plate theory. Galerkin's method is used to solve the governing equations.

To verify the accuracy of the computational model in this paper, the results obtained are compared with those of the existing literature. In addition, the effects of parameters such as the distribution pattern of elastic foundation, stiffness, geometrical parameters, temperature profile model, pore distribution, and GPLs pattern on the vibration characteristics of FGP-GPLs plates were investigated.

The results show that a reasonable foundation distribution pattern can significantly improve the stiffness of FGP-GPLs plates when the foundation area is the same. When the pore distribution and the GPLs pattern are asymmetric, the results of NTP versus uniform temperature profile (UTP) and linear temperature profile (LTP) differ significantly. The results of this study are informative for the structural design of FGP-GPLs plates supported by elastic foundations. In addition, the numerical results in this paper can be used as a reference for other researchers' studies.