Abstract
An analytical solution of a model problem of the flexural vibrations of a beam on an elastic Winkler foundation due to the front of a line load which moves along it is constructed. Quantitative results are presented for the special case when the velocity of the front is constant and the linear load is a step function. It is shown that a critical velocity of motion of the load exists and that, when this is exceeded, the elastic vibrations increase considerably. In this case, the dynamic range of deflection of the beam may be more than twice the magnitude of the displacement under the corresponding static load. The value of the critical velocity is determined by the mechanical properties of the beam and foundation and can be calculated using the ideal theory of an infinite beam. The amplitude of the deflection wave on approaching the critical velocity becomes larger as the length of the beam increases.
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