Vibrational motion of an elastic beam with prismatic and revolute joints

A dynamic model for the vibrational motion of an elastic beam with prismatic and revolute joints is presented. The Lagrangian approach in conjunction with the assumed modes technique is employed in deriving the equations of motion. The model developed accounts for all the dynamic coupling terms, as well as the stiffening effect due to the beam reference rotation. The tip mass dynamics is included together with the associated dynamic coupling between the modal degrees-of-freedom. In addition, the dynamic model devised takes into account the gravitational effects, thus permitting motions in either vertical or horizontal planes. Numerical simulations are performed and, whenever possible, comparisons with results of previous investigations are presented.