基于分数阶微分的金属橡胶迟滞非线性动力学模型  

Dynamic model for the nonlinear hysteresis of metal rubber based on the fractional-order derivative

作　　者：常宇健 田沃沃 陈恩利 申永军 邢武策 CHANG Yujian;TIAN Wowo;CHEN Enli;SHEN Yongjun;XING Wuce(Department of Electrical and Electronic Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;Department of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学电气与电子工程学院,石家庄050043 [2]石家庄铁道大学机械工程学院,石家庄050043

出　　处：《振动与冲击》2020年第14期233-241,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(11172183)。

摘　　要：金属橡胶元件的应力应变关系为非线性滞回曲线,现有的金属橡胶动力学模型大多采用多参数、分段函数进行描述,增加了系统的复杂性。通过分析金属橡胶的弹性恢复力和阻尼力的组成,利用分数阶微分能够描述各种材料及过程记忆性的特点,提出一种含有分数阶微分的金属橡胶黏弹性本构模型,在此模型基础上建立了金属橡胶非线性动力学系统模型;通过正弦位移加载实验获取了典型金属橡胶隔振系统在多种激励幅值、频率作用下的恢复力;采用遗传算法对实验数据进行曲线拟合,识别出模型中所有参数;通过分析推导出系统模型中各参数与振幅及频率的函数关系。结果表明,所提出的含分数阶微分项的金属橡胶非线性动力学系统模型,具有连续的数学表达式,能够较准确地反映金属橡胶非线性系统的完整动力学性能,而且与现有金属橡胶动力学系统模型相比,参数较少,结构简单,为金属橡胶动力学系统的研究提供了新的思路。The stress-strain characteristic of metal rubber components appears as a nonlinear hysteretic curve. Most of the existing dynamic models for metal rubber are described by multi-parameter and piecewise functions, increasing the complexity of the system.Making use of the fractional-order derivative which has been applied to the description of the memory characteristics of various materials and processes, a viscoelastic constitutive model for metal rubber with the fractional-order derivative was established through analyzing the composition of the elastic restoring force and the damping force of metal rubber. On this basis, a nonlinear dynamic system model for metal rubber was founded. The restoring force of a typical metal rubber vibration isolation system was analyzed through sinusoidal displacement loading experiments under various excitation amplitudes and frequencies. All the parameters of the model were identified by the curve fitting of the experimental data with the genetic algorithm. The functional relationships between the parameters of the system model and the amplitude and frequency were derived by a series of analysis. The results show that the nonlinear dynamic system model for metal rubber with a fractional order differential item can be described as continuous mathematical expressions,which can reflect the full metal rubber nonlinear system dynamic performance. The model involves less parameters and has a simpler structure compared to other existing metal rubber dynamics system models. The results provide a new way to the study of metal rubber dynamics systems.

关 键 词：金属橡胶 分数阶微分 非线性动力学 滞回特性 

分 类 号：V252.1[一般工业技术—材料科学与工程]