Nonlinear solutions for the steady state oscillations of a clamped-free rotating beam

Abstract

The rotating beam problem has been extensively used as a benchmark for testing nonlinear finite element implementations. The remarkable characteristic of this benchmark is the coupling between axial a transverse deformations due to the centrifugal forces. The rotating beam dynamics exhibits a centrifugal stiffening effect that can only be captured either by including a kinematic coupling between axial and transverse deformation or by using a nonlinear description of the elastic forces. This paper presents simplified models of the rotating beam that capture the centrifugal stiffening effect due to the inclusion of an axial to transverse kinematic coupling of the beam centreline. The simplified models allow a discussion on their accuracy and a meaningful analysis of the nonlinear oscillations present in the steady state rotation. The results of the simplified models are compared to finite element solutions obtained by using the absolute nodal coordinate formulation and a commercial FEM code.