形状记忆合金紧缩滞回型伪弹性的数学模型及振动分析

Mathematic Model of Shrink Hysteretic SMA and Its Vibration Analysis

研究形状记忆合金（ＳＭＡ）紧缩型伪弹性的数学模型，以一阶微分方程形式描述此类材料制成的减振降噪元件的恢复力模型，可以通过调节参数描述不同形态的恢复力－变形关系．在此模型基础上，分析由此类元件构成的减振系统在不同条件下的振动响应规律．结果表明，该数学模型不仅简单实用、普遍适用，而且能很好地描述这类非线性振动系统的特性．同时，此类减振装置对较强烈的振动有更好的抑制作用．

The mathematical model of the shrink pseudoelasticity of shape memory alloy (SMA) is investigated. The recovery of vibration reduction element made of SMA is described by means of the first-order differential equation. The model can describe different force-deformation relation by adjusting the parameters. Basing on this model, the vibration response of the vibration reduction system composed of a SMA spring and a mass is analyzed for different excitation conditions. The result shows that the mathematical model is not only simple, practical, universally applicable, but also can well describe the character of this kind of nonlinear vibration system. And this vibration reduction system is more effective in absorbing relatively intensive vibration.