Dynamic response of Timoshenko beam under moving mass

In this article, the dynamic responses of a Timoshenko beam subjected to a moving mass, and a moving sprung mass are analyzed. By making recourse to Hamiltonʹs principle, governing differential equations for beam vibration are derived. By using the modal superposition method, the partial differential equations of the system are transformed into a set of Ordinary Differential Equations (ODEs). The resulted set of ODEs is represented in state-space form, and solved by means of a numerical technique. The accuracy of the results has been ascertained through comparing the results of our approach with those available from previous studies; moreover, a reasonable agreement has been obtained. The quantities of the dynamic response of the beam for the case of moving sprung mass are confronted with moving mass and also moving load cases. Through extensive numerical campaign, it is concluded that with respect to the applied values of suspension system properties, the deflections of the beam subjected to moving load case are an upper bound for moving sprung mass results.