Dynamics of a cantilever beam attached to a moving base

Hybrid state-space time integration of rotating beams

“…The beam is originally introduced by [5], but parameters corresponding to [6] have been used. These are equivalent to a beam of length L = 10 m, with a square cross-section with side-lengths b = 0.0775 m. The beam is homogeneous and isotropic elastic with parameters E = 6.67 GPa and G = 2.00 GPa and mass density ρ = 200 kg/m 3 .…”

Simulation of a Moving Elastic Beam Using Hamilton's Weak Principle

“…The spin up is a simple maneuver that is commonly simulated in the literature for multibody dynamics programs [20,36]. For this maneuver, the 72-inch aluminum beam is attached to a hub (cantilevered) and accelerated from rest to 180 rpm (3Hz) about the z axis.…”

A Finite Element Study of the Geometric Centrifugal Stiffening Effect

“…For these problems and until recently, linear strain-displacement relationships were considered sufficient for the description of the small deformation. Kane et al [11] showed that under the described conditions, the results obtained using the floating frame of reference formulation incorrectly exhibit instability that is not present in the physical model. Simo and Vu-Quoc [18] demonstrated that, in the case of a rotating beam, linear theories predict inadmissible destabilization effects, even for extremely stiff beams.…”

“…In general, it is believed that the instability of the elastically linear models is due to the neglect of the coupling between the longitudinal and transverse displacements, so that the bending deformation of the beam does not cause any variation in the longitudinal displacement [11]. Wu and Haug [21] presented a solution based on substructuring the flexible bodies, and used bracket joints to impose the nonlinear connectivity conditions between the substructures.…”

“…They showed that a second-order theory solves the problem. While the cause for this instability has not been completely explained, several methods have been proposed to successfully solve the problem [3,4,6,11,18,19].…”