Modeling and chaotic motion of a shape memory alloy beam vibration model
Ge Gen1 Wang Hong-li2 ,Xu jia2
1. School of Mechanical Engineering, Tianjin Polytechnic University，Tianjin 300160, China2.School of Mechanical Engineering, Tianjin University, Tianjin 300072, China
Abstract：The vanderpol hysteretic cycle was applied to describe the hysteretic nonlinear characteristic of the strain-stress relation of a shape memory alloy （SMA）based on experimental data. A dynamical model with nonlinear damping of a simply supported SMA beam subject to axial excitation was proposed based on elastic theory and Galerkin’s approach. At first, the local bifurcations of the free vibration model were analyzed by the normal form theory. And the global bifurcation was studied Melnikov approach. Secondly, the undermined fundamental frequency and normal form method was utilized to study the influence of the disturbing parameters to the fundamental frequency. Finally, the improved Melnikov expression for the oscillator was built based on the results of the undermined fundamental frequency method and time scale transformation to obtain the approximate threshold value of chaotic motion in the Homoclinicity points of view. The numerical results show the efficiency of the theoretical analysis.
葛根;王洪礼;许佳. 形状记忆合金梁的建模及混沌阈值计算[J]. , 2012, 31(12): 103-107,.
Ge Gen Wang Hong-li;Xu jia. Modeling and chaotic motion of a shape memory alloy beam vibration model . , 2012, 31(12): 103-107,.
2012, Vol. 31 
