中心刚体-柔性梁耦合系统离散模型的研究

Study on discretization model of coupling dynamics system consisting of hub-flxible beam

采用数值仿真对由中心刚体、柔性梁组成的刚-柔耦合系统的动力学离散模型进行了研究。考虑到刚柔-耦合系统的控制方程没有精确解析解,只能寻求数值解,最广泛使用的离散方法是有限元,但其广义坐标数目过于庞大,因此本文探讨了采用经典结构动力学中不同边界的模态函数离散动边界下刚柔耦合动力学方程的可行性及各自的优劣,得到刚柔耦合系统的模态缩减规律。

In this thesis, discretization model of rigid-flexible coupling dynamics systems is studied. Modeling theory of rigid-flexible coupling dynamics systems has been studied for dozens of years. The accurate rigid-flexible coupling dynamics model has been established and corresponding governing equation of motions has been acquired. The equation is nonlinear, time dependent and strong coupling, so it is scarcely possible to acquire the exact analytical solution. Discretization is necessary to get the numerical solution. Finite-element-method （FEM） is widely used. While the number of generalized coordinates for the complex FMS by using the FEM is large, the mode-reduction-method （MRM） is more effective. It means that only lower order modes of the beam without large overall motions are chosen to reduce the number of the generalized coordinates. While the boundary conditions of the complex FMS don＇t usually fit a standard description. It is necessary to prove whether the classic mode-shape function effectively simulates the rigid-flexible coupling dynamics systems or not. In view of the issue mentioned above, this paper studies the feasibility and validity of using the classic mode-shape function to simulate the rigidflexible coupling dynamics system and analyse the effectivity of different boundary condition mode-shape function. Then the rule of MRM of a hub-beam system is gained. The analysis above proves the validity of MRM and gets the procedure of MRM.