形状记忆合金梁动力稳定性

基于形状记忆合金材料的热：力学行为和拟弹性行为本构关系及梁的动力学平衡方程，建立了该类梁横向振动非线性动力学模型．用平衡态定性分析法讨论了形状记忆合金梁的稳定性与材料相变的关系．研究表明，梁的横向振动平衡态的稳定性与材料相的稳定性有对应关系．在马氏体相稳定的低温状态，系统有3个不动点，1个为稳定中心，另外2个为不稳定鞍点；在马氏体与奥氏体共存的中间温度状态，系统有5个不动点，3个为稳定的中心，2个为不稳定的鞍点；在奥氏体相稳定的高温度状态，系统有唯一稳定不动点。

Dynamic Stability of a Shape Memory Alloy Beam

A nonlinear dynamics model was derived based on the constitutive equations of the thermo-mechanical and pseudoelastic behaviors of shape memory alloy (SMA) and the dynamic equilibriumequations of an SMAbeam. The analytic results showthat the transverse vibration stability of the beamcorresponds to the equilibriums of the phase transformations. At lower temperature where martensite isstable, there are three fixed points: one representing stable center and the other two describingunstable saddle points. At the middle temperature where both martensite and austenite coexist, thereare five fixed points: three representing stable centers and the other two describing unstable ddlepoints. At high temperature where austenite is the exclusive stable phase, there is only one fixed pointrepresenting a stable center.