Dynamic response of infinite periodic beam subjected to a moving load

A study is presented of the oscillation of an infinite beam which rests on identical periodic simple elastic supports. The beam transverse defection is caused by a harmonic concentrated force,moving steadily along the beam. It is supposed that the beam had been at rest before the force approached and returned to rest after the force had moved away. It is further supposed that the beam defections at any pair of points,separated on the periodic support spacing,obey the special condition. The beam defection is governed within the segment by the Euler-Bernoulli partial differential equation,four boundary conditions and the above mentioned suppositions. The Fourier transformation is used to solve the problem. Some numerical examples and corresponding analysis are presented. If the angular velocity of the moving load is small,then the beam inertia forces are small in comparison with its elastic ones. In this case,the beam defection has to be near the quasi static defection of the beam without inertia. Also,the value of beam defection increases as the oscillation frequency and the velocity of the movin load grow.