考虑附加质量的中心刚体—柔性悬臂梁系统的动力特性研究

DYNAMICS STUDY OF HUB-BEAM SYSTEM WITH TIP MASS

对考虑附加质量的中心刚体-柔性悬臂梁系统的动力特性进行研究。首先采用Hamilton原理和有限元离散 化方法,在计入柔性梁由于横向变形而引起的轴向变形的二阶耦合量的条件下,给出该系统的刚柔耦合动力学方 程(即一次近似耦合模型),以及相应的非惯性系下的动力学模型,然后通过数值仿真对系统的动力特性进行研究。 仿真结果显示,即使是小的附加质量也会对系统动力特性产生重要影响,附加质量使得梁的响应幅值变大和响应 频率降低,且会影响柔性梁和中心刚体的终点位置。附加质量的影响随系统大范围运动的角速度的增大而变大。 当系统大范围运动为低速时,传统的混合坐标模型仍然会导致较大误差;当系统大范围运动为高速时,传统的混 合坐标模型存在失效的可能。

Dynamic analysis of hub-beam system with a tip mass is investigated, where the beam is a flexible one. Firstly, by the Hamilton theory and using the finite element method for discretization, the rigid-flexible coupling dynamic model (i.e. the first-order approach coupling model) which takes the second-order coupling quantity of axial displacement caused by transverse displacement of the beam into account is presented. The corresponding dynamic model in non-inertia system (i.e. the zero-order approach coupling model) is presented as well. Then dynamic characteristics of the hub-beam system are studied through numerical simulations. Simulation results demonstrate that small tips mass may affect dynamic characteristics of the system. The tip mass may result in the largening of beam response and the falling of response frequency of the beam, and may affect the terminal positions of the beam and the hub as well. The effect of the tip mass becomes large along with the increasing of angular velocity of the large motion of the system. Even the angular velocity of the large motion is small, the traditional hybrid coordinate model may lead to big error. When the regular velocity of the large motion is large, there possibly exists failure in using the traditional zero-order approach model.