Embedded Shape Memory Alloy Wires Of A Composite Beam Vibration Control

By employing theoretical analysis and incorporating with numerical computation, small amplitude free vibration of thermal pre-buckled and post-buckled composite Euler -Bernoulli beams embedded with shape memory alloy wires is studied and the free vibration frequencies of beams versus temperature rise are presented. Firstly, based on Brinson's one-dimensional thermomechanical constitutive relations of shape memory alloys and by using mesomechanical analysis of composites, the one-dimensional thermomechanical constitutive equations of composite beams embedded with shape memory alloy wires and subjected to thermal load are established. Next, using the geometrically non-linear theory for axially extensible Euler-Bernoulli beams and the theory of free vibration of the beams, the general dynamic governing equations for free vibration of composite beams embedded with shape memory alloy wires and subjected to a uniform temperature rise field are set up. Then, the responses of all problems are expressed in two parts which are static thermal post-buckling solution and vibration solution. The small amplitude free vibration model near the thermal post-buckling configuration is presented. Finally, in the sense of small amplitude free vibration, the linear vibration responses of the composite beam embedded with NiTi shape memory alloy wires subjected to a uniform temperature rise are achieved by shooting method and the characteristic curves of the first to fourth-order frequencies versus temperature rise of the thermal pre-buckled and post-buckled composite beam at different SMA wires relative volume fraction are given. Numerical results show that the frequencies are increasing when the beam is in pre-buckled states and the frequencies are decreasing when the beam is in post-buckled states at the same temperature rise conditions if shape memory alloy wires were embedded in the beam. Shape memory alloy wires can increase the critical temperature of the beam, and also can restrain thermal buckling occurring or make the post-buckled beam back to initial equilibrium states. The results show that the free vibration frequencies can be tuned by SMA significantly and SMA martensitic transformation temperature, SMA wires relative volume fraction and initial pre-strain all have influence on the natural frequencies of the beam, which are important design parameters in the vibration control of structures.