ON THE OSCILLATIONS OF INFINITE PERIODIC BEAMS SUBJECTED TO A MOVING CONCENTRATED FORCE

Abstract A study is presented of the oscillation of an infinite beam which rests on identical periodic simple elastic supports. The study shows how a combination of two different approaches, the previous author's [1] and Mead's [2], allows one to remove an unnatural restriction on the parameters of the problem. The beam's transverse deflection 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 deflections at any pair of points, separated on the periodic support spacing, obey the special condition. This condition means that the steady beam oscillations take place and allows one to consider just one beam segment between neighbouring supports. The beam deflection 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.