Date of Award

Winter 2015

Degree Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Haiyan H. Zhang

Committee Chair

Haiyan H. Zhang

Committee Member 1

Qingyou Han

Committee Member 2

Richard Mark French

Committee Member 3

Xiuming Diao


The objective of this research is to utilize the frequency-dependent viscoelastic material model and characterize the dynamic response of rubber bushing under external excitation. Furthermore, with appropriate modeling, two heat generation mechanisms of rubber bushing are explored and their thermal fields are investigated. Due to the nonlinear force-deflection relationship of the viscoelastic material, finding satisfactory mechanical properties of rubber components still poses a great challenge. However, industry nowadays is in urgent demand for precise finite element analysis (FEA) modeling of rubber components. For example, a proper constitutive relationship of rubber components is critical to providing a reliable and trustable simulation of vehicle suspension systems. As for current FEA commercial software, the frequency-dependent modulus of viscoelastic material hasn't been presented well and they have failed to provide satisfactory results. Therefore, two approaches, FEA and the multi-body dynamic analysis have been selected together to give a more comprehensive and credible prediction of suspension system's performance in different working conditions. The FEA approach evaluated the stability of rubber bushing in view of the dynamic response and temperature distribution under high frequency excitation. With these results, the life prediction of rubber bushing becomes more feasible. The multi-body dynamic analysis explores the structure instability of rubber bushing when exposed to extremely high frequency and estimates the energy dissipation in the rubber core.^ The key innovations of this paper can be classified into four aspects. The first one is the application of multi-body dynamics in the dynamic analysis of rubber bushing. Based on experimental modal analysis, the sandwich cylindrical rubber bushing is treated as multi-body. With the multi-body model, the transfer function of the rubber bushing is calculated in order to estimate the dynamic response. The second innovation comes from the development of the FORTRAN program to solve the system transfer function of the structure made of viscoelastic material. Since the geometry and boundary conditions are amenable in FEA compared with the experimental modal testing, this approach is not just applicable in rubber bushing dynamic analysis, but also useful in dynamic analysis of different rubber components. The third innovative contribution of this research is connecting the multi-body analysis with continuum mechanics to evaluate the mechanical properties of rubber bushing. The last innovation is the structure-thermal coupling of rubber bushing to predict its temperature distribution based on the heat source calculated from the FEA simulation. The finite volume method (FVM) is applied using MATLAB in the simulation of temperature distribution. In this research, the classical standard linear model is applied in the FEA program to characterize the variation of viscoelastic material in the frequency domain. The three parameters of this model have been identified with the batch data measurement using dynamic mechanical analysis equipment (DMA). Specially, two heat generation mechanisms are explored to emphasize the friction-induced hysteresis damping except for the commonly discussed viscous damping. As complementation of FORTRAN program simulation in the frequency domain, the multi-physics commercial software COMSOL is employed to estimate the dynamic response of rubber bushing and temperature distribution in the time domain. To verify the results of FEA and multi-body dynamic approach in the dynamic and thermal analysis of rubber bushing, dynamic tests have been carried out using torsion and tensile testing machines. The experimental temperature distribution is in good agreement with the simulation results, which indicated the feasibility of the FEA method.^ However, due to the limited experience and complicated constitutive relationship of the viscoelastic material, the standard linear viscoelastic model is chosen to simulate the heat dissipation mechanism of rubber core. The high-frequency or high-temperature dynamic testing are almost impossible because of the experiment equipments' range of service. As the first step of predicting the dissipation energy density and temperature distribution of rubber components, the initial explorations are significant and provide a proper guidance for further predictions about life expectation.