Dynamic analysis of a beam subjected to an eccentric rolling disk

This paper presents a theory concerning the beam element subjected to an eccentric rolling disk (or simply called the eccentric-disk-loaded beam element) such that the dynamic responses of a beam subjected to an eccentric rolling disk with its inertia force, Coriolis force and centrifugal force considered can be easily determined. To this end, the property matrices of an eccentric-disk-loaded beam element are firstly derived by means of the Lagrange\'s equations. Then, the overall property matrices of the entire vibrating system are determined by directly adding the property matrices of the eccentric-disk-loaded beam element to the overall ones of the entire beam itself. Finally, the Newmark direct integration method is used to solve the equations of motion for the dynamic responses of a beam subjected to an eccentric rolling disk. Some factors relating to the title problem, such as the eccentricity, radius and rotating speed of the rolling disk, and the Coriolis force and centrifugal force induced by the rolling disk are investigated. Numerical results reveal that the influence of last factors on the dynamic responses of the pinned-pinned beam is significant except the centrifugal force.