Dynamics of three-dimensional beams undergoing large overall motion

In the previous linear formulation of flexible multibody system, the neglect of stiffening terms may cause significant error in case of high rotating speed. In this paper, a geometric nonlinear formulation of three-dimensional beams is proposed based on virtual power principle. Frequency results of a rotating spatial beam using the present nonlinear model are compared with those using the linear model without stiffening. An influence ratio, which is related to non-dimensional axial base acceleration and lateral angular velocity, is put forward to clarify the limit of the linear formulation. It is shown that the relative frequency error is closely related to the influence ratio. Finally, simulation of a flexible spatial manipulator is carried out to verify the effectiveness of the criterion.