磁流变阻尼器的分数阶模型及其减振系统分析

Fractional Calculus Modeling of the Magnetorheological Damper and the Analysis of its Damping System

研制了一种复合式磁流变阻尼器,它主要由橡胶弹簧、磁流变阻尼两部分组成,其性能兼具橡胶弹簧减振和磁流变阻尼减振的优点。引入了分数阶微积分理论,建立了复合阻尼器的分数阶Zener理论模型,并探讨了在该模型下的粘弹性。为验证该模型的有效性,将分数阶微积分应用到磁流变振动台系统建模上,建立了分数阶系统模型,并给出了分数阶系统传递函数描述,求出了位移函数。实验表明,减振系统的分数阶模型与实验数据能够较好的吻合,从而证明了分数阶模型在磁流变阻尼器的减振模型研究上的有效性。

The combined magnetorheological damper developed in the paper is composed of rubber spring,magnetorheological damper,which inherits the damping merits of the rubber spring and the magnetorheological damper.Here the factional-order constitutive equation was introduced to study the characteristics of the combined damper according to its viscoelasticity.A fractional Zener model for the damper is built,and its viscoelasticity is analyzed.In order to verify the effectiveness of the fractional Zener model,the fractional-order system model of magnetorheological vibrant platform was set up and the transfer function representation of fractional-order system was given,and the function of displacement was also obtained.Through the experiments it was found that the sampling data can fit the fractional-order system model well.It is indicated the fractional-order constitutive equation and the transfer function are feasible and effective for investigation of magnetorheological vibrant device.