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This resonant phenomenon occurs when exciting frequency of the moving load series is consistent with one of the free vibration frequencies of the bridge.
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It is noticed that dynamic solution of the plate subjected to moving loading series represented by Eq. (15) is similar to that of a simply supported beam under moving loading series [2, 5].
According to literatures [2, 5], one of the most important resonance conditions can be expressed as frac{{omega_{n} }}{2pi } = frac{V}{{d_{text{v}} }}jquad (j = 1,2,3 cdots ) (16 where number j can be explained as the production of the Fourier series expansion of generalized force induced by the moving loading series.
Both a single moving load and a series of equidistant moving loads are considered.
A single moving load or a series of moving loads representing a high-speed train was used by Yang et al. [8] and Savin [9] to identify the condition of resonance in the bridges.
From the point of view of time history, we might regard a moving load as a series of impact on continuum media during a number of tiny time intervals.
Next, an approximation of real-time responses was developed for the moving loads as periodic series.
Waves due to a moving load.
The temporal Fourier transform of the rail motion is expanded by a Fourier series with respect to the longitudinal coordinate, and then the response of the rail deflection due to a quasi-harmonic moving load is derived.
Using a series solution for the dynamic deflection in terms of normal modes the individual and coupling effect of the mass of the moving load, of its velocity and of other parameters is fully assessed.
Moving load effect on pavements is actual engineering problem.
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