CHAPTER 4 - Vibrations of Beams—II

Abstract

This chapter provides an overview of vibrations of beams. It discusses the complex practical problem of the vibration of bridges because of the passage of vehicles. The forces on the bridge due to a moving vehicle are of three types: (1) gravity forces; (2) inertia forces; and (3) disturbing forces due to unbalanced parts in the vehicle. The lines of action of these forces move across the bridge at a certain velocity. Practical problems lie between the following extreme cases. (1) The weight of the vehicle is large compared with that of the bridge, so that the system can be treated as a concentrated weight on a light elastic beam, i.e. as a single-degree-of-freedom system, but as the weight is moving across the beam, the stiffness of the system varies continuously. (2) The weight of the vehicle is small compared with that of the bridge, so that the system can be idealized as an elastic beam subjected to a moving force. This will be considered, subject to the assumptions that the beam is uniform, its ends are simply supported, and the velocity of the forceis constant.