Centrifugal and gyroscopic effects on dynamic response of rotating cantilever beams under step loading

Abstract

In this paper, a simplex finite element model for beams (FEMB) with a complete formulation is presented to study the dynamics of rotating cantilever beams subjected to distributed external loads. In our approach, the finite element method (FEM) and Timoshenko's beam theory is used. We will, particularly, examine the centrifugal and gyroscopic effects on the linear vibration of a rotating cantilever beam in stationary regime. In this model, extension, bending, and torsion degrees of freedom (DOF) are combined using a parameterization of the 3D motion of the beam by Euler's three-angle sequence. That allows identifying all the terms of the gyroscopic coupling in a more compact equations system. To ensure convergence, a sufficient number of finite elements are required in this model. The considered beam in the numerical simulation is pre-twisted and linearly tapered with a rectangular section. Results show that the dynamic centrifugal effect decreases the natural frequencies of the beam. Furthermore, the gyroscopic coupling induces rapid extension and torsion beatings when the beam undergoes a step bending load. Without damping, these beatings can persist and cause material fatigue.