大变形旋转柔性梁的一种高次刚柔耦合动力学模型

A HIGH-ORDER RIGID-FLEXIBLE COUPLING MODEL OF A ROTATING FLEXIBLE BEAM UNDER LARGE DEFORMATION 1)

对在平面内做大范围转动的中心刚体--柔性梁系统的刚柔耦合建模理论进行了深入研究,建立了系统的高次耦合动力学模型.该动力学模型考虑了柔性梁横向弯曲变形和纵向伸长变形,且在纵向位移中计及由于横向变形而引起的纵向缩短项,即非线性耦合变形项,并保留了与非线性耦合项相关的一些高阶项,最终得到了系统的高次刚柔耦合动力学方程.由此得到的动力学方程不仅能适用于柔性梁的小变形问题,也同样适用于大变形问题,弥补了一次近似耦合模型在处理柔性梁大变形问题上的不足.通过与绝对节点坐标法以及一次近似耦合模型的对比验证了高次耦合模型的正确性.

The dynamic modeling theory of a flexible beam which is rotating in a plane is further studied, and the high- order coupling dynamic model is investigated here. Both the transversal deformation and the longitudinal deformation of the flexible beam are considered. And the non-linear coupling deformation term, also known as the longitudinal shortening term caused by transversal deformation, is considered here. The high-order terms related to the non-linear coupling term are retained, which are ignored in the first-order approximation coupling modeling. Thus, we can get the rigid-flexible coupling dynamic equations of the system. The high-order coupling model can not only be used in small deformation case, but also in large deformation case. Then simulations, compared to the absolute nodal coordinate formulation and the first-order coupling model, are given to prove the validity of the high-order coupling model. And the results show that the high-order coupling model can make up for the deficiency of the first-order approximation coupling model in the large deformation situation.