Vibrations of a Double-Beam System with Intermediate Elastic Restraints Due to a Moving Force

Abstract

In this paper, we investigate the problem of the dynamic behaviour of a double-beam system with intermediate elastic restraints subjected to a moving point force. Problem is solved by replacing this type of structure with two single-span beams loaded with a given moving force and redundant forces representing reactions in the intermediate restraints. Redundant forces are obtained by solving Volterra integral equations of the second order which are compatibility equations corresponding to each redundant. Solutions for the arbitrarily supported singlespan beam loaded with a moving point force and concentrated time-varying force are given. Difficulties in analytically solving Volterra integral equations are bypassed by applying a simple numerical procedure. Finally, a numerical example of a double-beam system with two elastic restraints is presented in order to show the effectiveness of the presented method.