To improve the low-frequency vibration reduction effect of a steel spring floating slab track (FST), nonlinear quasi-zero-stiffness (QZS) vibration isolato

The viscoelastic-plastic dynamic properties of rail pads were are not adequately accounted for in the traditional vehicle–track coupled dynamic model. To investigate the influence of the viscoelastic-plastic dynamic properties of rail pads on the high-speed vehicle–track coupled vibrations, we obtained the viscoelastic-plastic dynamic properties of rail pads first by a series of laboratory tests, after which we described these properties theoretically by a modified Fractional Derivative Zener (FDZ) model and a traditional Berg friction model. A modified vertical vehicle–slab track coupled dynamic model was established by introduction of the modified FDZ and traditional Berg models for rail pads to investigate the influence of the viscoelastic-plastic dynamic properties of the rail pads on the high-speed vehicle–slab track coupled vibration responses under various preloads and temperatures. The FDZ and Berg models for rail pads improved the calculation accuracy of the high-speed vehicle–slab track coupled vibration responses, compared with the traditional KV model for rail pads, especially in the dominant high frequency range. The dynamic plastic properties of the rail pads effectively suppressed the high-frequency wheel-rail forces and yet increased the high-frequency vibration responses of the track substructures under the rail. Low temperatures and increased preloads on rail pads had a similar effect on the vehicle–track coupled vibrations. Increasing the preload on rail pads or decreasing the temperature increased the wheel-rail random excitation energy and its dominant frequencies, increased the vibration responses of the wheel-set and the track substructure under the rail, and decreased the vibrations of the rail at nearly all frequencies. Highlights

A hybrid Spectral Element Method (SEM)–Symplectic Method(SM) method for high-efficiency computation of the high-frequency random vibrations of a high-speed vehicle–track system with the frequency-dependent dynamic properties of rail pads is presented. First, the Williams-Landel-Ferry (WLF) formula and Fractional Derivative Zener (FDZ) model were, respectively, applied for prediction and representation of the frequency-dependent dynamic properties of Vossloh 300 rail pads frequently used in China's high-speed railway. Then, the proposed hybrid SEM–SM method was used to investigate the influence of the frequency-dependent dynamic performance of Vossloh 300 rail pads on the high-frequency random vibrations of high-speed vehicle–track systems at various train speeds or different levels of rail surface roughness. The experimental results indicate that the storage stiffness and loss factors of Vossloh 300 rail pad increase with the decrease in dynamic loads or the increase in preloads within 0.1–10,000 Hz at 20°C, and basically linearly increase with frequency in a logarithmic coordinate system. The results computed by the hybrid SEM–SM method demonstrate that the frequency-dependent viscous damping of Vossloh 300 rail pads, compared with its constant viscous damping and frequency-dependent stiffness, has a much more conspicuous influence on the medium-frequency (i.e. 20–63 Hz) random vibrations of car bodies and rail fasteners, and on the mid- (i.e. 20–63 Hz) and high-frequency (i.e. 630–1250 Hz) random vibrations of bogies, wheels and rails, especially with the increase in train speeds or the deterioration of rail surface roughness. The two sensitive frequency bands can also be validated by frequency response function (FRF) analysis of the proposed infinite rail–fastener model. The mid and high frequencies influenced by the frequency-dependent viscous damping of rail pads are exactly the dominant frequencies of ground vibration acceleration and wheel rolling noise caused by high-speed railways, respectively. Even though the existing time-domain (or frequency-domain) finite track models associated with the time-domain (or frequency-domain) fractional derivative viscoelastic (FDV) models of rail pads can also be used to reach the same conclusions, the hybrid SEM–SM method in which only one element is required to compute the high-order vibration modes of infinite rail is more appropriate for high-efficiency analysis of the high-frequency random vibrations of high-speed vehicle–track systems.

An in-situ test to obtain vertical, transversal and longitudinal ground velocities and accelerations caused by high-speed trains was performed alongside the Chinese high-speed railway line between Beijing and Shanghai. The test results indicate that due to excellent track quaity and consolidated infrastructure, whether if the train speed is below or above the Rayleigh wave speed, the dominant frequencies of both the vertical ground velocity and acceleration are both integral multiples of the trainload frequency generated by the centre distance of two neigbouring cars. The frequency-domain distribution of the ground velocity is more sensitive to soil stiffness than is the ground acceleration; this is especially the case for the first dominant frequency. Whether the frequency amplitudes of the vertical ground vibration are higher than the horizontal vibrations depends on the soil stiffness. The greater the soil stiffness, the higher is the frequency-range of the vertical ground vibration compared with that for the horizontal vibration, and the smaller is the difference between the three-dimensional frequency-weighted ground vibration level and the vertical vibration. Thus, effects of horizontal ground vibrations cannot be ignored when the foundation soil is soft.

The purpose of this research was to investigate and improve the accuracy of the existing slab-track mat (STM) specifications in the evaluation of the vibration reduction effect. The static nonlinearity and dynamic mechanical characteristics of three types of STMs were tested, and then a modified fractional derivative Poynting–Thomson (FDPT) model was used to characterize the preload and frequency dependence. A modified vehicle–floating slab track (FST) coupled dynamic model was established to analyze the actual insertion loss. The insertion loss error evaluated by the frequency-dependent tangent stiffness increased with the increase in STM nonlinearity, and the error obtained by the third preload tangent stiffness was usually greater than that of the second preload. Compared with the secant stiffness, the second preload frequency-dependent tangent stiffness was more suitable for evaluating STMs with high-static–low-dynamics (HSLD) stiffness. In order to reflect the frequency dependence effect and facilitate engineering applications, it is recommended that second preload tangent stiffness corresponding to the natural frequency of the FST be used for evaluation. Furthermore, the insertion loss of the STMs with monotonically increased stiffness decreased as the axle load increased, and the opposite was true for the STMs with monotonically decreased stiffness. The vibration isolation efficiency of the STMs with HSLD stiffness was both stable and better than that of the STMs with monotonic stiffness.