Limit-Cycle Oscillation of Shape Memory Alloy Hybrid Composite Plates at Elevated Temperatures

Abstract

A traditional composite plate impregnated with pre-strained shape memory alloy fibers and subject to combined thermal and aerodynamic loads is investigated to demonstrate the effectiveness of using the SMA fiber embeddings in improving the static and dynamic response of composite plates. The problems investigated can be categorized into: thermal buckling subject to aerodynamic loading, linear flutter boundary at elevated temperatures, nonlinear flutter limit-cycle, and chaotic oscillations at elevated temperatures. A nonlinear finite element model based on the von Karman strain displacement relations and first-order shear deformable plate theory is derived. Aerodynamic pressure is modeled using the quasi-steady first-order piston theory. The governing equations are obtained using the principle of virtual work based on thermal strain being a cumulative physical quantity. Newton-Raphson iteration is employed to obtain the static aero-thermal large deflection at each temperature step and the dynamic response at each time step of the Newmark numerical integration scheme. A frequency domain solution is presented for predicting the flutter boundary at elevated temperatures, while the time domain method along with modal transformation is applied to numerically investigate periodic, non-periodic, and chaotic limit-cycle oscillations. The results show that the critical buckling temperature of the plate is greatly increased, and hence the thermal post-buckling deflection is suppressed by using SMA fiber embeddings. The SMA fiber embeddings caused an increase in the critical dynamic pressure at elevated temperatures, and enlargement of the static flat and dynamically stable region of the panel.