Limit-cycle Oscillations of Functionally Graded Material Plates Subject to Aerodynamic and Thermal Loads

Abstract

The nonlinear flutter and thermal buckling of a functionally graded material (FGM) plate panel subjected to combined thermal and aerodynamic loads are investigated using a finite element model based on the thin plate theory and von Karman strain-displacement relations to account for moderately large deflection. The thermal load is assumed to be steady-state constant temperature distribution, and the aerodynamic pressure is modeled using the quasi-steady first-order piston theory. The governing nonlinear equations of motion are obtained using the principle of virtual work adopting an approach based on the thermal strain being a cumulative physical quantity to account for temperature dependent material properties. The static nonlinear equations are solved by Newton-Raphson numerical technique to get the thermal post-buckling deflection. The dynamic nonlinear equations of motion are transformed to modal coordinates to reduce the computational efforts. The Newmark implicit integration scheme is employed to solve the second order ordinary differential equations of motion. Finally, the buckling temperature, post-buckling deflection and the nonlinear limit-cycle oscillations of an FGM panel are presented, illustrating the effect of volume fraction exponent, dynamic pressure, temperature rise, and boundary conditions on the panel response.