Nonlinear Vibration of Rotating Corotational Two-Dimensional Beams With Large Displacement

Abstract

In this paper, the nonlinear vibrations of rotating beams with large displacements are investigated by the use of the co-rotational (C-R) finite element method. In the C-R approach, the full motion is decomposed into a rigid body part and a pure deformational part by introducing a local coordinate system attached to the element. The originality we propose in this study is to derive its formulation in a rotating reference frame and include both centrifugal and gyroscopic effects. The nonlinear governing equations are obtained from Lagrange's equations using a consistent expression for the kinetic energy. With this formulation, the spin-stiffening effect from geometrical nonlinearities due to large displacements is accurately handled. The proposed approach is then applied to several types of mechanical analysis (static large deformation, modal analysis at different spin speeds, and transient analysis after an impulsive force) to verify its accuracy and demonstrate its efficiency.