Prediction of the dynamic equivalent stiffness for a rubber bushing using the finite element method and empirical modeling

A hybrid method using an approximation that is based on the finite element analysis and empirical modeling is proposed to analyze the dynamic characteristics of a rubber bushing. The hyperelastic–viscoplastic model and an overlay method are used to obtain the hysteresis of the rubber bushing in the finite element analysis. A spring, fractional derivatives, and frictional components are used in the empirical model to obtain the dynamic stiffness in wide ranges of the excitation frequencies and amplitudes. The parameters of the proposed empirical model are determined using the hysteresis curves that were obtained from the finite element analysis. The dynamic stiffness of the rubber bushing in the wide ranges of the frequencies and amplitudes was predicted using the proposed hybrid method and was validated using lower arm bushing experiments. The proposed hybrid method can predict the dynamic stiffness of a rubber bushing without the performance of iterative experiments and the incurrence of a high computational cost, making it applicable to analyses of full-size vehicles with numerous rubber bushings under various vibrational loading conditions.