Chaotic vibration of a shape memory alloy beam subjected to an axial dynamic load

In this paper, the dynamic behaviors of a shape memory alloy beam subjected to an axial dynamic load is studied. Based on the constitutive description of the thermo-mechanical and pseudo-elastic behaviors of the shape memory alloy material and the dynamic equilibrium equation of beam, the nonlinear dynamic model which dominates the transverse vibration of the beam is established first. And then the relations between the dynamic stability of the beam and the equilibrium of the material phase are investigated by using the qualitative analysis method of a differential dynamic system. Finally, the effects of the temperature and the axial load parameter and also the environmental damp on the chaotic behaviors of the system are investigated by using numerical simulation. It is found that the dynamic stability of the transverse vibration of the beam is consistent with the stability of material phase. At a temperature where both martensite and austensite coexist, the chaotic characteristic is the strongest and an increase in the value of load parameter is related to an increase in the chaotic motion, but an increase in the value of damp parameter is related to a decrease in chaotic behaviors.