形状记忆合金弹簧振子的非线性自由振动

Nonlinear Free Vibration of the Shape Memory Alloy Spring Oscillator

采用多项式本构方程描述形状记忆合金弹簧的恢复力,建立了单自由度形状记忆合金弹簧振子的非线性动力学模型,讨论该系统各平衡点的稳定性,并采用龙格-库塔法进行数值计算,分析该系统自由振动的特征。研究结果表明,系统在不同温度条件下有不同的平衡点,平衡点的稳定性由系统的阻尼系数和温度共同决定。在低温和中温条件下,系统自由振动具有对初始条件的敏感性,系统阻尼的存在可能改变系统的振动形式;而高温条件下,系统仅作衰减振动,运动规律受初始条件影响不大,但受阻尼影响较大。

The recovery force of shape memory alloy spring is described by using polynomial constitutive equation.The nonlinear dynamic model of the single-degree-of-freedom shape memory alloy spring oscillator is established.The stability of equilibrium points of this system is discussed.Numerical simulations are performed by a fourth-order Runge-Kutta method and the free vibration of the system is analyzed.The results show that the system has different equilibrium points at different temperatures and their stability is determined by temperature and damping coefficient.At the low temperature and medium temperature,the free vibration of the system is sensitive to initial conditions so that the existence of the system damping is likely to change its vibration forms.However,at the high temperature,the system can only perform the attenuate vibration so that its motion rules can subject not to much initial conditions but to more damping effects.