基于形状记忆合金的X形板阻尼器的力学模型

根据超弹性形状记忆合金（SMA）的分段线性化本构关系,建立了X形SMA板式阻尼器的力学模型;通过MATLAB程序进行数值模拟,绘制了X形SMA板的阻尼力滞回曲线,并研究了位移幅值、温度、形状尺寸对阻尼器基本特征参数（等效割线刚度、单位循环消耗的能量、等效阻尼比）的影响。结果表明：X形SMA板式阻尼器具有“旗帜”形的滞回曲线,耗能较小,但复位能力好;随位移幅值增加,耗能力和等效阻尼比增加,等效割线刚度降低,温度的影响与此相反;阻尼器的特征参数随板高增加均呈降低趋势;增加板宽,单位循环耗能与等效割线刚度增加,而等效阻尼比不变。研究结果为X形SMA板式阻尼器的设计和工程应用提供了理论依据。

Mechanical Model of X Type SMA Plate Damper

According to the piecewise linear consitutive model of superelastic shape memory alloy(SMA),the mechanical model of X type SMA plate damper is set up.By means of numerical simulation with MATLAB software,a damping force hysteresis loop is presented,and the influence of displacement amplitude,temperature and dimensions on damper's characteristics such as equivalent secant stiffness,energy dissipation for each cycle and equivalent damping ratio is investigated.The results show that the hysteresis loop displays "little banner" with lower energy absorption and better recentering capabilites.The increased displacement amplitude leads to increases in the energy dissipation and equivalent damping ratio,but decreases in the equivalent stiffness.The contray effects on the superelastic damping can be produced by the increase of temperature.As the plate height increases,the damper's characteristics all decrease.Besides,the greater width plate can dissipate more energy and take on greater equivalent stiffness,but have the constant equivalent damping ratio.The research results provide theoretical principles for the X type SMA plate damper's design and application in practical engineering.