Dynamic response of a non-classically damped beam with general boundary conditions subjected to a moving mass-spring-damper system

Abstract

In this paper a semi-analytical approach to efficiently determine the dynamic response of an Euler-Bernoulli beam with general boundary conditions crossed by a mass-spring-damper (MSD) system is presented. Based on a dynamic substructuring technique (DST), the non-classically damped beam subsystem in modal state space representation is coupled with the interacting degrees of freedom of the MSD system by applying a generalized corresponding assumption. This assumption implies equal displacements of the beam and the MSD system at the contact points. The resulting set of coupled equations of motion in state space has time-dependent system matrices. Special attention is paid to the appropriate formulation of the arrival and departure conditions of the MSD system on the beam. In an application example, the dynamic response of a viscoelastically supported beam with a lumped mass at both ends crossed by a MSD system is analyzed, examining the effect of the speed and various parameters of the viscoelastic supports. The comparison of the results of the coupled beam-MSD system and a less expensive approach, in which the MSD system is simplified by its static axle loads, shows the importance of explicitly considering the interaction between beam and MSD system for accurate response prediction.