Stability of an infinite beam on visco-elastic foundation under a uniformly moving distributed mass
Journal
Journal of Sound and Vibration
Journal Volume
521
Date Issued
2022
Author(s)
Abstract
The stability of a distributed mass of finite length travelling uniformly on an infinite beam resting on a visco-elastic foundation is considered in this paper. The focus is placed on the effects of the length of the distributed mass on the stability of the mass-beam-foundation system. It is argued that on the stability boundary, the mass-beam-foundation system is in the form of a steady state periodic motion. To seek the periodic solution, the infinite beam is divided into three segments, in each of which the differential equation is solved analytically. By comparing the stability boundary curves of the distributed mass of finite length with the one of infinite length, it is found that the stability boundary curves of finite length do not converge to the one of infinite length. It is believed that the course of the failure to converge towards the infinite length model is the differences in the boundary conditions at infinity. On the other hand, the stability boundary curves of finite length do converge to the point mass model when the mass length approaches zero. Compared to the point mass model, the distributed mass model is less stable. More precisely, for a specified system damping and total mass, the critical speed is in general much smaller if distributed model is adopted. The longer the mass length, the smaller the critical speed is. In short, the conventional point mass model overestimates the stability of the mass-beam-foundation system. ? 2021 Elsevier Ltd
Subjects
Distributed mass of finite length
Infinite beam
Stability boundary
Foundations
System stability
Beam foundations
Boundary curves
Elastic foundation
Finite length
Foundation systems
Infinite beams
Point mass models
Stability boundaries
Visco-elastic
Boundary conditions
SDGs
Type
journal article