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Floating slab track is an effective countermeasure to mitigate undesirable vibrations caused by metro trains. In this work, a stochastic fractional derivative model is proposed for simulating the dynamic behavior of rubber bearings in floating slab tracks. The stochastic fractional derivative model is based on the Grünwald representation of fractional calculus, the number theoretical method, and the probability density evolution method (PDEM). It considers the viscoelastic characteristics of the rubber bearings, as well as randomness in mechanical behavior due to manufacturing tolerances, aging, and fatigue. The stochastic fractional derivative model is then implemented into a vehicle–floating slab track coupled dynamics model to investigate the vibration isolation performance of the floating slab track with rubber bearings. The characteristics and advantages of the stochastic fractional derivative model with deterministic parameters are illustrated by comparing the results with the conventional Kelvin model. Finally, stochastic analyses of the dynamic response and the vibration isolation performance of the floating slab track are carried out using the coupled vehicle–floating slab track system dynamics model. Results show that the stochastic simulation of the vehicle–floating slab track system using PDEM is efficient and reliable compared with the Monte Carlo method. Thus, the proposed model is effective and useful for evaluating the vibration levels in floating slab tracks with uncertain parameters, and for predicting the reliability of the vibration isolation performance.

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