Vibration Analysis of Variable Cross Section Timoshenko Beams Resting on Flexible Foundation Under Two Travelling Loads

Abstract

Dynamic behavior of variable cross section Timoshenko beams resting on elastic foundation and subjected to two travelling loads is investigated. The vibrating system of beam structure and the simultaneous equations were treated using Galerkin and integral transform techniques. Closed form solution was obtained for both the transverse displacement response and the rotation the variable cross section Timoshenko beams under the travelling loads. From the analytical and numerical results, as the magnitude of foundation stiffness increases, the deflection profile of the Timoshenko beam decreases. Likewise, amplitude of deflection diminishes as the distance between the loads increases. The state at which the structure-load system experience resonance condition is established.