ON THE MAXIMUM AMPLIFICATION FACTOR OF A MOVING POINT FORCE ON A SIMPLE BEAM

Abstract

The dynamic behaviour of a simply supported beam traversed at constant velocity by a point force is thoroughly reviewed. In this work it is shown that the maximum dynamic amplification factor of a simple beam under a travelling point force is 1.74 times the static displacement due to that point force statically applied at the middle cross section of any simply supported beam. Besides it is also shown that this maximum amplification factor of 1.74 occurs at x=0.53 times the length of the beam ℓ when the load has reached the point 0.76ℓ and it corresponds to a velocity of 0.625 times the currently termed “resonance” velocity.