A new FEM approach for analysis of beams with relative movements of masses

The dynamics of beam–moving mass systems is considered. A ‘composite’ beam element is introduced, which explicitly identifies the Coriolis and centripetal effects dependent on the given current relative velocity of the particular mass. These effects are then mimicked in the numerical procedure by applying certain fictitious transversal and axial forces only to the elements being currently traversed by the masses.It is shown that the approach proposed is capable of recreating accurately and efficiently several analytical solutions reported in the literature and obtained mostly for a beam and masses moving with constant velocities, the cases pertaining to simulating a bridge–traveling vehicles interaction. The importance of the Coriolis and centripetal effects on the beam's response is quantified in terms of the parameters representing the dimensionless mass and its dimensionless velocity.Finally the interaction of a disturbed beam with a mass moving in a cyclic pattern is analyzed resulting in attenuation and amplification phases of the beam's vibrations, as expected. This case, for which an accurate recreation of the Coriolis effects is crucial, demonstrates that the approach can also be used for control purposes to explore numerically the possibilities of eliminating the system's vibrations by properly synchronized relative motion of its components.