旋转柔性悬臂梁动力学的Bezier插值离散方法研究*

摘要

在旋转柔性梁变形场描述中，引入Bezier插值离散方法。首先构建旋转运动悬臂梁物理模型，接着采用第二类Lagrange动力学方程和Bezier插值离散方法，在计入柔性梁横向弯曲变形引起的纵向缩短的情况下，推导了旋转柔性梁的刚柔耦合动力学方程，并编制旋转柔性梁的动力学仿真软件，然后通过仿真算例对系统的动力学问题进行研究。最后将仿真结果与有限元法、假设模态法进行分析比较，验证了提出的Bezier插值离散方法的正确性，并得出Bezier插值离散法的计算效率较高；计算精度符合工程实际需要，高速时计算精度大于假设模态法； Bezier插值离散方法在处理大柔性问题时比假设模态法合理。因此在多体系统动力学领域具有优良性能和应用价值的Bezier插值离散方法将具有推广价值。%The Bezier interpolation is introduced as a new discretization method for the rotating flexible beam deformation. First, the model of the rotating flexible beam is built. Then, the rigid-flexible coupling dynamic equations are established via employing the second kind of Lagrange’s equation. The longitudinal deformation and the transverse deformation of the flexible beam are considered, and the coupling term of the deformation which is caused by the transverse deformation is included in the total longitudinal deformation;and a software package for the dynamics simulation of the flexible beam is developed. Finally, the simulation results of the Bezier interpolation are compared with those of the assumed method and the finite element method. Simulation results demonstrate that the computational efficiency of the Bezier interpolation is the highest, the computational accuracy of Bezier interpolation is in accordance with the needs of engineering, and is higher than the one of assumed mode method in high-speed case. The Bezier interpolation method is better than the assumed mode method in dealing with the large deformation dynamics problem. So the Bezier interpolation method will be hopeful to win popularity in the field of multi-body system dynamics.