In this paper, fast Fourier transform and complex analysis are used to analyze the dynamic response of slabs on a viscoelastic foundation caused by a moving harmonic load. Critical speed and resonance frequency of the slab to a moving harmonic load are obtained analytically. It is proved that there exists a bifurcation in critical speed. One branch of critical speed increases as load frequency increases, while the other branch of critical speed decreases as load frequency increases. There are two critical speeds when the load frequency is low, but only one critical speed exists when the load frequency is high. A parametric study is also performed to study the effect of load speed, load frequency, material properties of the slab and the damping coefficient on dynamic response. It is found that the damping coefficient has significant influence on dynamic response. For small damping, the maximum response of the slab increases with increased load speed and frequency. However, for large damping, the maximum response of the slab decreases with increased load speed and frequency.

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