Research on dynamic stiffness with the high-order fractional derivative model for rubber bushing

A hybrid strategy for predicting the dynamic stiffness of rubber bushing is proposed in this study to analyze the axial amplitude-frequency dependence with the high-order fractional derivative model. Firstly, the finite element model (FEM) is constructed to calculate the force-displacement hysteresis curves under certain conditions. Secondly, a parametric model composed of the elastic element, the friction element, and the high-order fractional derivative viscoelastic element in parallel is proposed to describe the axial amplitude-frequency dependent behavior of rubber bushing. Then, based on the hysteresis curve obtained by the finite element analysis, the parameters of the high-order fractional derivative viscoelastic model are identified by using an adaptive chaos particle swarm optimization (ACPSO). Finally, the effectiveness of the proposed strategy is evaluated through simulations under sinusoidal excitation in the amplitude range of 0.1–2.0 mm and the frequency range of 0.1–25.0 Hz. The simulation results show that the parametric model can accurately estimate the dynamic stiffness under the condition of large amplitude and wide frequency. The hybrid strategy is practically useful for the dynamic stiffness estimate of rubber bushing, and reduces time and computational resources compared with the finite element method.