Random Response of Shape Memory Alloy Hybrid Composite Plates Subject to White-Gaussian Noise and Thermal Environment

Abstract

The random response and thermal buckling of a traditional composite plate impregnated with pre-strained shape memory alloy (SMA) fibers subjected to combined thermal and acoustic loads are investigated using a finite element model based on the first order shear deformable plate theory and von Karman straindisplacement relations to account for moderately large deflection. The thermal load is assumed to be steady state constant temperature distribution, and the acoustic excitation is considered to be a stationary Gaussian pressure with zero mean and uniform magnitude over the plate surface. The governing nonlinear equations are obtained using the principal of virtual work adopting an approach based on the thermal strain being an integral quantity of the thermal expansion coefficient with respect to temperature 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 transferred 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 random response of a SMA hybrid composite plate panel are