Dynamic characteristic and stability analysis of a beam mounted on a moving rigid body

摘要

The phenomenon of dynamic stiffening has drawn general interest in flexible multi-body systems. In fact, approximately analytical, numerical and experimental research have proved that both dynamic stiffening and dynamic softening can occur in flexible multi-body systems. In this paper, the nonlinear dynamic model of a beam mounted on both the exterior and the interior of a rigid ring is established by adopting the general Hamilton's variational principle. The dynamic characteristics of the system are studied using a theoretical method when the rigid ring translates with constant acceleration or rotates steadily. The research proves theoretically that both dynamic stiffening and dynamic softening can occur in both the translation as well as the rotation state of multi-body systems. Furthermore, the approximate vibration frequency, critical value and post-buckling equilibria of the translational beam with constant acceleration are obtained by employing the assumed modes method, which validates the theoretical results. The L-2 norm stability of the trivial equilibrium of the system with the external beam and the L-infinity norm stability of the bending of the external beam are proved by employing the energy - momentum method.