基于分数阶导数的金属橡胶动态特性建模

Dynamic Characteristic Model of Metal Rubber Using Fractional Derivations

金属橡胶材料具有非线性和黏弹性的动态特性。本研究用三次非线性函数描述其非线性特性,用分数阶三元模型描述其黏弹性,即分别用经典三元模型与分数阶三元模型,结合金属橡胶动态试验数据进行模型参数识别,发现分数阶三元模型能更准确地描述金属橡胶黏弹性力。不同振幅下金属橡胶迟滞曲线的拟合结果表明,分数阶模型可以较好地拟合不同工况条件下金属橡胶的迟滞曲线,为金属橡胶材料动态特性建模提供理论参考。

Metal rubber possesses the dynamic characteristics of nonlinearity and viscoelasticity.A cubic nonlinear function for the nonlinear elastic force and a fractional function for the viscoelastic force are.established in this paper to describe the dynamic characteristics.The classical ternary model and fractional ternary model were respectively adopted,in which the corresponding parameters derived from the metal rubber dynamic tests were identified.It was found that the fractional order ternary model more accurately describes the metal rubber elastic force.The fitting results of the metal rubber hysteresis curves under different amplitude show that the fractional order model can be better fitted under different working conditions.The whole work can provide theoretical reference on the dynamic characteristics of metal rubber material.