Divergence and flutter analyses of functionally graded porous trapezoidal plates reinforced with graphene platelets under thermal loading

In this article, the divergence and flutter behaviors of functionally graded (FG) porous trapezoidal plates reinforced with graphene platelets (GPLs) subjected to the supersonic airflow and thermal loading are investigated. It is assumed that porosity and graphene platelets are distributed in the thickness direction according to the functionally graded distributions. The material properties of FG porous reinforced with graphene platelets are estimated to be temperature-dependent. Three types of temperature distributions as uniform, linear and nonlinear temperature distributions in the thickness direction are considered. Using Hamilton's principle, the governing equations of motion are derived in the Cartesian coordinates based on the first order shear deformation theory (FSDT) as well as the linear piston theory. Also, the linear stability or divergence equations are obtained according to the principle of minimum total potential energy and adjacent equilibrium criterion. Using a mapping, the divergence and flutter partial differential equations and the associated boundary conditions in the Cartesian coordinates are converted to ones in the trapezoidal coordinates. Applying the generalized differential quadrature (GDQ) method and the state space technique, the transformed equations with the corresponding boundary conditions are solved to find the critical flutter aerodynamic pressure as well as the critical divergence temperature difference. The effects of various parameters such as porosity coefficient, symmetric and asymmetric porosity distribution, GPL distribution patterns, temperature differences and boundary conditions are studied on the stability region. The present results of this study can be used to design and manufacture the advanced aerospace vehicles at supersonic speeds and temperature changes.