On vibration and stability analysis of porous plates reinforced by graphene platelets under aerodynamical loading

The vibration and stability analyses of functionally graded (FG) reinforced porous plates with piezoelectric layers under supersonic flow are investigated. The plate has a FG core reinforced by nanocomposite graphene platelets (GPLs) which surrounded by two piezoelectric layers. The GPLs are distributed thorough the thickness direction both uniformly and non-uniformly. The first-order shear deformation plate theory (FSDT) and first-order piston theory are applied to analyze the stability of FG porous plates. Using Hamilton's principle and Maxwell's equation, the governing equations of motion as well as electrical and mechanical boundary conditions are obtained. Applying the Galerkin approach, the partial differential governing equations are converted to the ordinary differential equations. The numerical results show that the flutter aerodynamic pressure and natural frequencies decrease as the porosity coefficient increases. Besides, the symmetric porosity distribution together with GPL pattern A predicts the highest flutter aerodynamic pressure and natural frequencies. Also, the best efficient way to increase the stability region is considering GPL pattern A, with dispersing more GPLs fillers near the top and bottom surfaces of FG porous plate along with symmetric porosity distribution. Furthermore, FG porous plate enclosed by piezoelectric layers in open circuit condition predicts higher flutter aerodynamic pressure and natural frequencies than similar plate in closed circuit condition.