Abstract
The dynamics of a flexible beam which is rotating in a plane is further studied in this paper. The dynamic model of the rigid-flexible coupling system under large deformation is established and here by the dynamic simulation is also carried out. In this dynamic model not only the transversal bending deformation and the longitudinal deformation (including the axial stretching deformation and the longitudinal shortening term caused by the transversal bending deformation) of the flexible beam are considered, but also the curvature e ect induced by the longitudinal deformation is included. In the previous studies the bending deformation energy of the beam is usually expressed in terms of the bending deformation directly without considering the longitudinal deformation e ect. To take into account the influence due to the longitudinal deformation on the bending deformation energy of the beam the precise curvature formula in the form of parametric equation expressed in the floating frame of reference is used to calculate the bending deformation energy. And consequently the rigid-flexible coupling dynamic model of the system with the said the longitudinal deformation induced curvature e ect (LDICE) model is obtained. To validate the algorithm presented in this paper, several dynamic simulation examples are given. The results show that the dynamic model presented in this paper can not only be used in the analysis of the small deformation dynamics, but also in the large deformation dynamics, and indicate that the dynamic model with the curvature e ect obtained in this paper is more suitable to solve for the large deformation dynamic problems than the high-order coupled (HOC) model presented in the existing literature. The results obtained using the proposed model are compared with the results obtained using the absolute nodal coordinate formulation (ANCF) which is suitable for large deformation problems, and consequently validate the dynamic model proposed in this paper.
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