Pseudoelastic effect in autoparametric non-ideal vibrating system with SMA spring

In this paper a three degrees of freedom autoparametric system with limited power supply is investigated numerically. The system consists of the body, which is hung on a spring and a damper, and two pendulums connected by shape memory alloy （SMA） spring. Shape memory alloys have ability to change their material properties with temperature. A polynomial constitutive model is assumed to describe the behavior of the SMA spring. The non-ideal source of power adds one degree of freedom, so the system has four degrees of freedom. The equations of motion have been solved numerically and pseudoelastic effects associated with the martensitic phase transformation are studied. It is shown that in this type system one mode of vibrations might excite or damp another mode, and that except different kinds of periodic vibrations there may also appear chaotic vibrations. For the identification of the responses of the system＇s various techniques, including chaos techniques such as bifurcation diagrams and time histories, power spectral densities, Poincare maps and exponents of Lyapunov may be used.

形状记忆合金弹簧振子强迫振动的分岔与混沌

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。

波动温度环境下形状记忆合金梁的参激振动控制

引入形状记忆合金多项式本构模型描述材料的热力学行为,导出形状记忆合金梁在横向周期力扰动下的非线性动力学控制方程,从而研究合金梁在波动变化温度场中的参数激励振动控制。数值分析表明,温度对形状记忆合金梁的弹性模量和振动特性影响很大,且利用最大Lyapunov指数法可以获得临界温度值,当温度在该临界温度值附近波动时可以实现形状记忆合金梁的参数激励振动控制。最后,讨论临界温度值受外激励振幅和频率的影响,从而拓展所提出方法的实际应用。