Aeroelastic flutter of post-buckled functionally graded panels

Functionally graded materials (FGMs) with continuously varied composition effectively reduce the mismatch at bonding surface between different constituents. As thermal protection structures, functionally graded panels (FGPs) eliminate the internal thermal stress concentration which arises from aerodynamic heating. The aeroelastic flutter boundary of an FGP is analyzed considering the structural geometric nonlinearity due to thermal post-buckling deflection. The effective FGM properties are calculated using the rule of mixture homogenization with the power law distribution assumption. The first-order shear deformable plate theory, von Karman strain-displacement relations and the first-order piston theory are adopted to formulate the nonlinear aeroelastic finite element equations of FGPs in supersonic flow according to the principle of virtual work. The numerical simulation results of thermal post-buckling response are obtained using the Newton-Raphson iterative method, and the mechanism of post-buckling deflection affected by the airflow is discussed. The panel flutter boundary is determined by analyzing the stability of post-buckling equilibriums. It is concluded that the symmetry of a ceramic-metal FGP is destroyed by through-the-thickness material distribution, and the panel tends to buckle to the metal side under in-plane thermal stresses. The position of maximum post-buckling deflection moves to the down-stream in the supersonic airflow, and the post-buckling deflection decreases with the increase of flow dynamic pressure. The geometric nonlinearity increases the flutter critical dynamic pressure of post-buckled FGPs when the large post-buckling deflection is occurred at relative high temperature and low non-dimensional dynamic pressure flow. However, the geometric nonlinearity is not so important at high non-dimensional dynamic pressure flow because the post-buckling deflection is restrained to a small one by the supersonic airflow.