Dynamic Response of a Double-Beam System Subjected to a Harmonic Moving Load

The dynamic behavior of a double-beam configuration subjected to a harmonic moving load was studied in this paper. The model was built to represent the wheel–track system that was composed of two infinite Timoshenko beams joined by uniformly spaced sleepers and supported by a continuous viscoelastic foundation. The response of the coupled beams to a moving harmonic excitation was first derived, after which the wheel–rail interaction was incorporated through a generalized Fourier series formulation. The associated Fourier coefficients were obtained from a finite system of algebraic equations imposed by the wheel–track contact conditions. The numerical simulation was carried out to compare the predictions of the Timoshenko and Euler–Bernoulli beam assumptions and to explore the influence of load speed and excitation frequency on the dynamic characteristics of the double-beam system. Comparative analysis reveals that Timoshenko beam theory predicts larger vertical displacements for rail, slab, and sleeper near the model’s cut-off frequencies (20 Hz and 30 Hz) than Euler–Bernoulli theory, with higher load velocities reducing the first cut-off frequency and amplifying peak amplitudes. The dynamic response exhibits two critical velocities at sub-cut-off frequencies, where rail displacements increase with load velocity, whereas this trend reverses when the load frequency meets or exceeds the cut-off frequencies, and no distinct peaks occur at 25 Hz and 40 Hz. The research findings are of great significance for the vibration propagation and vibration disaster prevention for shield tunnels during the train operation.