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

发布时间：2019-04-02 02:54

【摘要】：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.
[Abstract]:In this paper, the dynamics of flexible beam system with central rigid body which rotates in a wide range in plane is studied. The dynamic model of rigid-flexible coupling system considering large deformation effect is established, and the dynamic simulation is carried out. The dynamic model takes into account not only the transverse bending deformation and longitudinal deformation of flexible beams (including the longitudinal shortening caused by axial tensile deformation and transverse bending deformation), but also the effect of longitudinal deformation on curvature. Called curvature longitudinal deformation effect. In previous studies, the transverse bending deformation of flexible beams is usually expressed directly by the transverse bending deformation of flexible beams, without considering the effect of longitudinal deformation. In order to consider the effect of longitudinal deformation of flexible beam on transverse bending deformation energy, the exact curvature formula in the form of parameter equation of flexible beam is used to calculate the bending deformation energy of flexible beam in floating coordinate system. On this basis, a rigid-coupled dynamic model based on floating coordinate system considering the effect of longitudinal deformation of curvature is established. A numerical simulation example is given to verify that the dynamic model presented in this paper can be applied to both small and large deformation problems of flexible beams, and that the dynamic model proposed in this paper is suitable for both small and large deformation problems of flexible beams. Compared with the existing high-order rigid-flexible coupling dynamic model, it is more suitable for the treatment of large deformation problems. The correctness of the model is verified by comparing with the absolute node coordinate method which can deal with the large deformation of flexible beams.
【作者单位】：南京理工大学理学院;上海交通大学工程力学系;
【基金】：国家自然科学基金(11272155,11132007) 江苏省“333工程”(BRA2011172) 中央高校基本科研业务专项资金(30920130112009)资助项目
【分类号】：O313.3

【参考文献】