采用粘弹性分数导数模型的橡胶隔振器动态特性的建模及应用  

MODELING AND APPLICATIONS OF DYNAMIC CHARACTERISTICS FOR RUBBER ISOLATORS USING VISCOELASTIC FRACTIONAL DERIVATIVE MODEL

作　　者：吴杰[1] 上官文斌[1] 

机构地区：[1]华南理工大学汽车工程学院,广州510641

出　　处：《工程力学》2008年第1期161-166,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(50575073);汽车安全与节能国家重点实验室开放基金项目(KF2006-06)

摘　　要：橡胶隔振器的动态特性与激振振幅及激振频率相关。给出一个可以表征橡胶隔振器动态特性与激振振幅及激振频率相关性的模型,其中,用摩擦力模型表征其动态特性与振幅的相关性,用分数导数粘弹性模型表征其动态特性与频率的相关性。计算分析了所建立的模型与目前广泛采用的两种描述橡胶隔振器动态特性模型(基于Maxwell的模型和粘性阻尼模型)在表征其与激振振幅及激振频率的相关性;使用分数导数和Kelvin-Voigt模型时,计算分析了一个含有橡胶隔振器的单自由度振动系统的自由振动和阶跃激励的时域响应。计算结果表明:采用分数导数模型能更加准确地描述橡胶隔振器的动态特性,建立的模型可以用于含有橡胶隔振器的振动系统的动态特性分析。Measurements show that dynamic characteristics of the rubber isolators relate to excitation amplitudes and excitation frequencies. A model characterizing the relations between excitation frequencies as well as excitation amplitudes and the dynamic performances of a rubber isolator are presented. The amplitude dependency is characterized by adding friction effects and the frequency dependency is included by a viscoelastic fractional derivative element. The estimated dynamic characteristics of the rubber isolator using the proposed model are compared with those estimated using two frequently used models （models based on a Maxwell model and a Dashpot model）. A single-degree-of-freedom system with a rubber isolator is used to calculate the response of a mass under the free and step excitations when the rubber model is characterized with the proposed model and the Kelvin-Voigt model, respectively. The calculated results show that the proposed model is efficient over the two frequently used models in estimating the frequency-and amplitude-dependent dynamic characteristics of a rubber isolator. Thus the proposed model can be used to analyze dynamic response of a system with rubber isolators.

关 键 词：振动理论 橡胶隔振器 粘弹性分数导数 动态特性建模 动态特性分析 

分 类 号：O328[理学—一般力学与力学基础]