THE EFFECT OF SHAPE MEMORY ALLOY EMBEDDINGS ON THE NONLINEAR FLUTTER OF COMPOSITE PANELS SUBJECT TO THERMAL AND RANDOM ACOUSTIC LOADS

Abstract

Shape memory alloys (SMAs) refer to a group of materials that have a unique ability to recover large pre-strains completely when heated above certain characteristic temperature called the austenite finish temperature. During the strain recovery process, a large tensile recovery stress occurs if the SMA is restrained. In this work, a traditional composite plate impregnated with pre-strained shape memory alloy fibers and subject to the combined effect of thermal, aerodynamic, and acoustic 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 are: thermal buckling, aerothermal buckling, linear flutter at elevated temperatures, flutter nonlinear limit­ cycle and chaotic oscillations at elevated temperatures, nonlinear random vibration under thermal effect, and nonlinear flutter-random vibration at elevated temperatures. A new nonlinear finite element model, based on the first-order shear deformable plate theory, is derived. von Karman strain displacement relations are utilized to account for geometric nonlinearity. The aerodynamic pressure is modeled using the quasi-steady first-order piston theory, while the random acoustic pressure is modeled using a white-Gaussian acoustic wave. The governing equations are obtained using the principle of virtual work. The nonlinear temperature dependence of material properties for the composite matrix and SMA fibers is considered in the formulation. 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. An eigenvalue problem is solved at each temperature step to predict the natural frequencies of the thermally buckled plate. A frequency domain solution is presented for predicting the flutter boundary at elevated temperatures, and an updated eigen-solution procedure is adopted to obtain the harmonic limit­ cycle oscillation amplitude at a given dynamic pressure and temperature rise.