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<p>This paper concentrates on nonlinear dynamic behaviors of a longitudinal vibration system within rail vehicles subjected to combined harmonic and stochastic excitations. An integrated research framework is established, combining piecewise analytical derivation, stochastic numerical algorithms, and quantitative criteria. First, a piecewise nonlinear model describing the three-stage operational characteristics of the coupler buffer is developed based on Hamiltonian system theory, with explicit parametric expressions derived for its homoclinic and heteroclinic orbits. Subsequently, the stochastic averaging method and the Fokker-Planck-Kolmogorov (FPK) equation are employed to obtain the stationary probability density function of the system’s response amplitude, allowing the quantitative determination of critical conditions for stochastic D-bifurcations and P-bifurcations. Furthermore, a stochastic Melnikov computation method tailored for piecewise systems is proposed. Through piecewise integration, spectral transformation, and mean-square analysis, a quantitative criterion for predicting chaos thresholds is established. Numerical simulations are performed using a customized Euler-Maruyama stochastic algorithm, and theoretical predictions are verified through multi-faceted analyses, including phase portraits, Poincaré sections, time histories, and frequency spectra. The results demonstrate strong agreement between theoretical predictions and numerical outcomes. This study elucidates the complex nonlinear mechanisms of the system and provides a quantitative basis for chaos suppression and safety control in engineering applications.</p>

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Dynamical behaviors in a longitudinal vibration system of rail vehicles under combined stochastic excitations

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Sengen Hu,
  • Liangqiang Zhou

摘要

This paper concentrates on nonlinear dynamic behaviors of a longitudinal vibration system within rail vehicles subjected to combined harmonic and stochastic excitations. An integrated research framework is established, combining piecewise analytical derivation, stochastic numerical algorithms, and quantitative criteria. First, a piecewise nonlinear model describing the three-stage operational characteristics of the coupler buffer is developed based on Hamiltonian system theory, with explicit parametric expressions derived for its homoclinic and heteroclinic orbits. Subsequently, the stochastic averaging method and the Fokker-Planck-Kolmogorov (FPK) equation are employed to obtain the stationary probability density function of the system’s response amplitude, allowing the quantitative determination of critical conditions for stochastic D-bifurcations and P-bifurcations. Furthermore, a stochastic Melnikov computation method tailored for piecewise systems is proposed. Through piecewise integration, spectral transformation, and mean-square analysis, a quantitative criterion for predicting chaos thresholds is established. Numerical simulations are performed using a customized Euler-Maruyama stochastic algorithm, and theoretical predictions are verified through multi-faceted analyses, including phase portraits, Poincaré sections, time histories, and frequency spectra. The results demonstrate strong agreement between theoretical predictions and numerical outcomes. This study elucidates the complex nonlinear mechanisms of the system and provides a quantitative basis for chaos suppression and safety control in engineering applications.