To provide a theoretical basis for eliminating resonance and optimizing the design of viscoelastically supported bridges, this paper investigates the analytical solutions of train-induced vibrations in railway bridges with low-stiffness and high-damping rubber bearings. First, the shape function of the viscoelastic bearing reinforced concrete (RC) beam is derived for the dynamic response of the viscoelastic bearing RC beam subjected to a single moving load. Furthermore, based on the simplified shape function, the dynamic response of the viscoelastic bearing RC beam under equidistant moving loads is studied. The results show that the stiffness and damping effect on the dynamic response of the supports cannot be neglected. The support stiffness might adversely increase the dynamic response. Further, due to the effect of support damping, the free vibration response of RC beams in resonance may be significantly suppressed. Finally, when the moving loads leave the bridge, the displacement amplitude of the viscoelastic support beam in free vibration is significantly larger than that of the rigid support beam.

Numerical simulation of the electrical conductivity of carbon fiber-reinforced asphalt concrete is essential for understanding its electrical behavior, yet research in this area remains limited. This study prepared six groups of Marshall specimens with carbon fiber (CF) contents of 0.1 wt%, 0.2 wt%, 0.3 wt%, 0.4 wt%, 0.5 wt%, and 0.6 wt%. The resistivity and asphalt concrete (AC) impedance spectra were measured to analyze the effect of fiber content on electrical performance. Nyquist diagrams were fitted to establish an equivalent circuit model, and a representative volume element (RVE) finite element model was developed. The Generalized Effective Medium (GEM) equation was employed to fit the resistivity data. The results show that the resistivity exhibits a two-stage characteristic—an abrupt decrease followed by stabilization, with an optimal CF content range of 0.2–0.4 wt%. Among the equivalent circuit parameters, the contact resistance (R₁) and tunneling resistance (R₂) significantly decreased, the growth of interface capacitance (C₁) slowed, the constant phase element Z_Q increased, and the non-monotonic change of volume resistance (R₃) reflected the heterogeneity of the internal void distribution of the material. The finite element numerical solution for resistivity, derived from the GEM equation, aligns well with experimental values, validating the proposed simulation approach.

In order to explore the vibration mechanism of vibration damping composite floor slabs and further enrich the theory of floor slab vibration calculation, the free vibration characteristics of vibration damped composite floor slabs and the dynamic response of vibration damped composite floor slabs under multi-source excitation is analyzed using first type Chebyshev polynomials to construct the displacement function and derive an analytical solution. The three-dimensional laminated theory is employed, considering the interlayer interaction. Based on the proposed method, the influences of loading types, positions, magnitudes, and frequencies on the vertical vibration of floor slabs are calculated. The study illustrates that, under the action of multi-source excitation, the displacement and acceleration responses calculated by the method proposed in this paper are always greater than those calculated by the single-plate theoretical solution. The dynamic responses of the vibration damping composite floor slab decrease with the increase of the thickness and elastic modulus of the vibration damping layer. Under different thicknesses of the vibration damping layer, the peak accelerations of the vibration damping composite floor slabs increase linearly with the growth of the load amplitude. In addition, the load movement path has a significant effect on the vibration response of the floor slab. When the moving load moves along the short side of the floor, the displacement response of the floor is generally greater than that along the long side of the floor.