Nonlinear flutter response of pre-heated functionally graded panels

The thermo-mechanical behavior of functionally graded (FG) panels is investigated in supersonic air flow. The three-node triangular element based on the Mindlin plate theory is employed to account for the transverse shear strains, and the von-Karman nonlinear strain-displacement relation is utilized considering the geometric nonlinearity. The effective material properties of the FG material are assumed to vary through the thickness according to simple power law distribution. The aeroelastic equation is established using the first-order piston theory, the linear rule of mixture and the principle of virtual work. A multi-mode approach is utilized to form the reduced-order model. Nonlinear flutter response is obtained by solving the reduced-order aeroelastic equation in time using the Runge-Kutta fourth-order method. Numerical simulation reveals that the multi-mode reduced-order model has a good convergence property. By using the 24-mode model the variation of flutter amplitude with dimensionless dynamic pressure, and the route of nonlinear flutter response from simple harmonic limit cycle oscillation (LCO) to non-harmonic periodic oscillation are examined.