考虑曲率纵向变形效应的大变形柔性梁刚柔耦合动力学建模与仿真

对在平面内做大范围转动的中心刚体柔性梁系统的动力学进行了研究,建立了考虑大变形效应的系统刚柔耦合动力学模型,并进行了动力学仿真.该动力学模型不但考虑了柔性梁横向弯曲变形和纵向变形(包含轴向拉伸变形和横向弯曲变形而引起的纵向缩短项),还考虑了纵向变形对曲率的影响,称为曲率纵向变形效应.在以往的研究中,柔性梁的横向弯曲变形能往往直接使用柔性梁横向弯曲变形来表达,并没有考虑纵向变形的影响.为了考虑柔性梁纵向变形对横向弯曲变形能的影响,在浮动坐标系下使用柔性梁参数方程形式的精确曲率公式来计算柔性梁的弯曲变形能.在此基础上建立了基于浮动坐标系的考虑曲率纵向变形效应的刚耦合动力学模型.论文给出了数值仿真算例,验证了本文所建的动力学模型既能适用于柔性梁的小变形问题,又能适用于大变形问题,且较现有高次刚柔耦合动力学模型更加适用于大变形问题的处理.论文还通过与能处理柔性梁大变形问题的绝对节点坐标法的比较,验证了模型的正确性.

RIGID-FLEXIBLE COUPLING DYNAMIC MODELING AND SIMULATION WITH THE LONGITUDINAL DEFORMATION INDUCED CURVATURE EFFECT FOR A ROTATING FLEXIBLE BEAM UNDER LARGE DEFORMATION

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 deforma-tion (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 effect 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 effect. 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 effect (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 effect 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.