基于超弹性、分数导数和摩擦模型的碳黑填充橡胶隔振器动态建模

DYNAMIC MODELING FOR CARBON-FILLED RUBBER ISOLATORS BASED ON HYPERELASTIC ITY, FRACTIONAL DERIVATIVE AND A GENERALIZED FRICTIONAL MODEL

碳黑填充橡胶隔振器(以下简称"橡胶隔振器")的动态特性与预载、激振频率和激振振幅相关。实验测试了一橡胶隔振器的动态特性,建立了基于超弹性、分数导数和摩擦模型的橡胶隔振器动态特性的非线性模型,其中超弹性模型用于描述橡胶隔振器的弹性,分数导数模型用于表征橡胶隔振器动态特性的激振频率相关性,摩擦模型用于表征橡胶隔振器动态特性与激振振幅相关的特性,文中论述了建模方法和参数辨识方法。有限元分析获得橡胶隔振器的静态力-位移曲线,利用测试得到的橡胶隔振器在大振幅、低频激励下的力-位移关系,拟合得到橡胶隔振器动态模型中摩擦模型的参数,利用测试得到的橡胶隔振器在小振幅、高频激励下的力-位移关系,拟合得到橡胶隔振器动态模型中分数导数模型的参数。利用建立的模型和拟合得到的参数计算分析了橡胶隔振器动态特性的振幅相关性、频率相关性和预载相关性,并与实验结果进行了对比分析。分析结果表明,建立的模型可以较好的描述橡胶隔振器的动态特性。

The measured dynamic characteristics of a carbon-filled rubber isolator (CFRI) are dependent on static preload, excitation amplitude and frequency. A non-linear model that can characterize the frequencyits and amplitude dependent performances of a CFRI is presented. A hyperelastic constitutive model is applied to model its elastic force, a fractional derivative model is used to model its frequency dependent property, and a generalized frictional model is imposed to model its amplitude dependent performance. The methods estimating the model parameters are illustrated in detail. Static elastic force versus displacement is obtained by a FE analysis. The parameters of the model describing its amplitude dependent performance are obtained from the measured relation between force and displacement under low-frequency and large-amplitude excitations. While the parameters characterizing its frequency dependent property are estimated by least square fittings for its measured dynamic stiffness and loss angle under high-frequency and small-amplitude excitations. Finally, the formulae for the proposed model are obtained. The calculated dynamic characteristics of the CFRI with the proposed model are compared with the identified model parameters by experiments. It is shown that the proposed model can estimate the dynamic performances of a CFRI under different excitation amplitudes and frequencies.