Modeling And Analysis Of Low Frequency Dynamic Characteristics Of Silicone-oil-filled Rubber Isolator Based On Fractional-Differential Constitutive Theory

In practical engineering applications,the silicone-oil-filled rubber isolator normally presents better vibration isolation performance than ordinary rubber isolator.This isolator is usually composed of a cylindrical rubber isolator coupling with a viscous damper with an annular hole.The high-viscosity silicone oil in viscous dampers has complex viscous and elastic properties and obviously shows frequency and amplitude dependent characteristics.In this paper,the dynamic viscoelastic characteristics of the isolator are studied by different modelling methods.This paper proposed that the coupled isolator was modelled by separating into two portions,the rubber portion and silicone oil portion,respectively.The Kelvin-Voigt model was used to describe the dynamic characteristics of rubber portion,and four models,Maxwell model,Zener model,fractional Maxwell model and fractional Zener model,were used to model the silicone oil portion.The complex stiffness characteristics of these models were analyzed in frequency domain,and compared with the experimental results.The results showed that the Kelvin-Voigt model could better fit the dynamic characteristics of the rubber portion.The fractional derivative models could better describe the dynamic characteristics of the silicone oil portion than the classical models,and the fractional Zener model could make up the stiffness of the fractional Maxwell model.Meanwhile,in order to better understand the physical characteristics of the silicone oil portion of the isolator,the time domain method was used to numerically solve the force-displacement relationship of the fractional Zener model.Compared with the experimental results,it showed that the fractional Zener model could well describe the frequency dependence of the silicone oil portion.Also,a superposition of two forces,a fractional Maxwell force and a Duffing-type elastic force,was used to model the silicone oil portion.It was found that this model could capture both the frequency and amplitude dependent properties of the isolator.In addition,the silicone oil portion was modelled according to the basic principles of fluid mechanics.The silicone oil was regarded as a fractional Maxwell fluid.Based on the assumption that the annular orifice fluid was incompressible,the fluid mechanics model considering rheological properties of silicone oil was derived.Then,combining the Grünwald-Letnikov difference equation with the fourth-order Runge-Kutta numerical algorithm,an improved Runge-Kutta numerical algorithm was proposed to solve the first-order fluid system in the time domain.And compared with the conventional Maxwell model,simulation results showed an advantage for describing the dynamic behavior of the isolator.Finally,using fractional Zener model to describe silicone oil portion,a single-degree-of-freedom vibration isolation system with silicone-oil-filled rubber isolator was established.The dimensionless motion equation was derived.And response characteristics were obtained,including frequency response function,force transmissibility,amplification factor and phase difference.The influence of damping ratio and fractional order on the these response characteristics was analyzed to improve the vibration isolation efficiency.Research in this paper has important theoretical significance and application values for accurately describing the dynamic characteristics of viscoelastic isolators,guiding the design of isolator parameters and predicting the performance of vibration isolation systems.