Thermo-acoustic random response of temperature-dependent functionally graded material panels

A nonlinear finite element model is provided for the nonlinear random response of functionally graded material panels subject to combined 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 first-order shear-deformable plate theory with von Karman geometric nonlinearity and the principle of virtual work. 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. Newton-Raphson iteration method is employed to obtain the dynamic response at each time step of the Newmark implicit scheme for numerical integration. Finally, numerical results are provided to study the effects of volume fraction exponent, temperature rise, and the sound pressure level on the panel response.