Dynamic response of Timoshenko beam under moving mass

In this article, the dynamic responses of a timoshenko beam subjected to a moving mass, anda moving sprung mass are analyzed. by making recourse to hamilton's principle, governing differentialequations for beam vibration are derived. by using the modal superposition method, the partial differentialequations of the system are transformed into a set of ordinary differential equations (odes). the resultedset of odes is represented in state-space form, and solved by means of a numerical technique. theaccuracy of the results has been ascertained through comparing the results of our approach with thoseavailable from previous studies; moreover, a reasonable agreement has been obtained. the quantities ofthe dynamic response of the beam for the case of moving sprung mass are confronted with moving massand also moving load cases. through extensive numerical campaign, it is concluded that with respect tothe applied values of suspension system properties, the deflections of the beam subjected to moving loadcase are an upper bound for moving sprung mass results.