Investigation on nonlinear and fractional derivative Zener model of coupled vehicle-track system

Abstract

ABSTRACTThe nonlinear and fractional derivative Zener model of viscoelastic material considering Berg’s friction force model is established, which can be used to describe the frequency-dependent and amplitude-dependent behaviour of rubber isolator. The simplified Berg’s friction force scheme was proposed to improve computational efficiency in the frequency domain. The frequency response of the single degree of freedom system modelled with the fractional derivative Zener model and the proposed simplified Berg’s friction force scheme was investigated, and it agrees well with the results calculated by discrete Fourier transform. In addition, the fractional derivative Zener model and the proposed simplified Berg’s friction force scheme are implemented to model the rail pads and the primary suspension rubber spring in a railway vehicle, and then the nonlinear and fractional derivative Zener model of the coupled vehicle-track system was established. The frequency response calculated by the proposed nonlinear and fractional derivative Zener model of coupled vehicle-track system was compared to the calculation using ordinary Kelvin–Voigt model, and the results have shown that there is little difference in the calculation results between the two models, but the vibration responses of bogies, wheelsets and rails are quite different in time domain and frequency domain. Furthermore, the comparison between the proposed model and the fractional derivative Kelvin–Voigt model were analysed. The difference between the two models is small in the frequency range from 1 to 200 Hz and in the whole time domain, but the difference is large in the high frequency region. The proposed nonlinear and fractional derivative Zener model of the coupled vehicle-track system has high efficiency and accuracy both in time domain and frequency domain.Abbreviations: FDZ: fractional derivative Zener; SBFF: simplified Berg’s friction force; CVTS: coupled vehicle-track system; DFT: discrete Fourier transform; SDOF: single degree of freedom; FDKV: fractional derivative Kelvin–Voigt.