旋转楔形-回形梁的高次动力学建模和末端变形分析

对四种不同结构中心刚体-柔性Euler Bernoulli梁系统进行刚柔耦合动力学分析．其中以等截面梁、变截面梁、等截面回形梁、变截面回形梁为对象，研究楔形梁及回形梁对系统的末端变形位移影响．变截面梁的宽高尺寸沿着轴向线性变化．梁的变形包含了轴向、横向、耦合变形项（横向弯曲引起的纵向缩短）．采用假设模态法和第二类Lagrange方程建立系统的动力学方程，并用C++编写软件进行动力学仿真．研究表明：在相同条件下，梁的截面尺寸及空心部分对梁末端变形位移影响十分明显，且当梁在较大变形情况下，该高次耦合模型依然能得到正确的结果，因此在针对实际结构建模时，建立符合实际截面的模型至关重要．

A High-Order Dynamic Model and End Deformation Analysis of a Rotating Tapered Hollow Beam

The rigid-flexible coupling dynamic analysis of flexible hub-beam systems with different beam structures is carried out. The influences of the tapered and the hollow geometries on the deformation of the tip of the beam system are studied considering the uniform section beam, gradient section beam, uniform section hollow beam and gradient section hollow beam. The width and height of the gradient section beam vary linearly along the axial direction. Both the transversal and the longitudinal deformations of the flexible beam are considered. For the longitudinal deformation, the non-linear coupling term, also known as the longitudinal shortening caused by transversal deformation, is considered. The assumed mode method is adopted to describe the deformation field of the tapered beam and Lagrange's equations of second kind is used to deduce the kinetic equations of the system. Dynamic simulation is carried out.by developing C++ coded software. The research shows that under the same conditions, the cross-section size and the hollow geometry of the beam have a significant effect on the deformation displacement at the tip of the beam. The proposed high order coupling model can still lead to correct results when the beam is in large deformation. Therefore, it is very important to establish a model that accords with the actual configuration when modeling the actual structures.