Vibration and Stability of a Shallow Arch Under a Moving Mass-Dashpot-Spring System

Abstract

In this paper we study the dynamic behavior of a shallow arch under a moving load system containing two masses, a dashpot, and a suspension spring. It is assumed that the masses in the load system are under the action of gravity. This paper is an extension of a previous publication in which the arch is loaded by a moving point force. The emphasis of the paper is placed on finding out how the inertia effect of the load system affects the dynamic response of the arch. It is found that the point-force model is a good approximation only when the arch is slender and the moving speed of the load system is low. The boundary of a dangerous speed zone is defined based on the comparison of the total energy gained by the arch and an energy barrier. It is observed that the suspension model predicts a considerably different dangerous speed zone from the one predicted by the point-force model, especially in the high-speed range.