中文摘要：

采用多项式本构方程描述形状记忆合金弹簧的恢复力,建立了形状记忆合金弹簧振子强迫振动的非线性动力学模型。采用龙格-库塔法进行数值计算,给出了系统随量纲一温度、量纲一阻尼系数及量纲一激振力幅值的分岔图和对应的Lyapunov指数谱,分析了系统随这些参数的分岔行为。此外,通过不同参数组合下的位移时程图、相图以及Poincare截面图,分析了系统的周期运动和混沌运动。结果表明：通过改变温度、阻尼系数和激振力幅值等参数,可以使系统实现周期运动或混沌运动,从而可实现对系统振动的控制。

英文摘要：

The recovery force of shape memory alloy spring was described by using polynomial constitutive equation.A nonlinear dynamic model of forced vibration for the shape memory alloy spring oscillator was established.Numerical simulations were performed by a fourth-order Runge-Kutta method.The bifurcation diagram and Lyapunov-exponent spectrum were presented while the dimensionless temperature,the dimensionless damping coefficient or the dimensionless amplitude of exciting force was varied respectively,thus the bifurcation of the system was investigated.Furthermore,the periodic and chaotic motions were analyzed by means of the displacement time history diagram,the phase portrait and the Poincare section diagram with different parameters.The results show that the periodic or chaotic motion of the system occurred by changing temperature,damping coefficient and amplitude of exciting force,thus the vibration of the system can be controlled.