Supersonic Flutter of Functionally Graded Panels Subject to Acoustic and Thermal Loads

Abstract

A nonlinear finite element model is provided for the supersonic flutter behavior of functionally graded material panels subject to combined aerodynamic, thermal, and random acoustic loads. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are derived using the classical plate theory with von Karman geometric nonlinearity and the principle of virtual work. The first-order piston theory is adopted to model aerodynamic pressures induced by supersonic airflows. The thermal load is assumed to be steady-state constant temperature distribution, and the acoustic excitation is considered to be a stationary white-Gaussian random pressure with zero mean and uniform magnitude over the plate surface. The governing equations are transformed to modal coordinates to reduce the computational efforts. The Newton-Raphson iteration method is employed to obtain the dynamic response at each time step of the Newmark scheme for numerical integration. Finally, numerical results are provided to study the effects of the volume fraction exponent, aerodynamic pressure, temperature rise, and the random acoustic load on the panel response.