Revisiting the Moving Mass Problem: Onset of Separation Between the Mass and Beam

Abstract

In the moving mass problem, the interaction force between a moving mass and structure obviously depends on the velocity of moving mass and the flexibility of structure. Thus, in some situations, the interaction force may become zero to change its sign, which implies the onset of the separation between the moving mass and structure. Most investigations on this subject have missed or ignored the possibility of the onset of separation in solving the dynamic responses of structures excited by moving masses. Hence, this paper investigates the onset of the separation between the moving mass and beam, and then takes into account its effect in calculating the interaction forces and also in calculating the dynamic responses of the beams considered herein. It is shown that the separation between the moving mass and structure can occur more easily and has unnegligible effects on the dynamic responses of the structure as the mass ratio (M/ml) increases, especially at high velocity of moving mass. Thus, for accurate prediction of the dynamic response of a structure excited by a moving mass, the effect of separation must be taken into account in the analysis.