Non-linearly dynamic modelling of an axially moving beam with a tip mass

摘要

In this paper, the equations of motion for a deploying beam with a tip mass are derived by using Hamilton's principle. In the dynamic formulations, the beam is divided into two parts. One part of the beam is outside the rigid support and is free to vibrate, while the remaining part is inside the support and is restrained from vibrating. Four dynamic models: Timoshenko, Euler, simple-flexible and rigid-body beam theories, are used to describe the axially moving beam. An external force, parallel to the direction of the axially moving motion, is applied at the left-hand side of the flexible beam. It is found that the axially moving motion and flexible vibrations are non-linearly coupled in the system equations. Finally, the effects of several conditions on the rigid-body motion and the flexible are discussed. (C) 1998 Academic Press. [References: 19]