基于Bezier插值方法的作大范围旋转运动锥形悬臂梁动力学研究

研究了作大范围旋转运动高度和宽度均沿着梁长度方向变化的锥形悬臂梁动力学问题.采用Bezier插值方法对柔性梁的变形场进行描述,考虑柔性梁的纵向拉伸变形和横向弯曲变形,计入由于横向弯曲变形引起的纵向缩短,即非线性耦合项.运用第二类拉格朗日方程推导出作旋转运动锥形梁的动力学方程,并编制了动力学仿真软件,对作旋转运动锥形梁的频率和动力学响应进行研究.结果表明:不同锥形梁截面的动力学响应和系统频率将有明显差异,因此对实际系统合理建模,将能得到更为精确的结果.

Dynamic analysis of a rotating tapered cantilever beam based on bezier curve interpolation

The natural frequencies and the dynamic response of a rotating tapered cantilever Euler Bernoulli beam were investigated. The height and the width of the tapered beam vary linearly along its length. The approach of Bezier curve interpolation was used to describe the deformation of the flexible beam. Both the transversal and the longitudinal deformations of the flexible beam were considered. And in the total longitudinal deformation, the non linear coupling term, also known as the longitudinal shortening caused by transversal deformation, was considered. The rigid flexible coupling dynamic equations of the system were established via employing the second kind of Lagrange's equation. A software package for the dynamic simulation of the rotating tapered cantilever beam was developed. Then the natural frequencies and the dynamic response of the rotating tapered cantilever beam were investigated and compared. The simulation shows that dynamics response and natural frequencies of different tapered beams will be significantly different. Reasonable modeling of the actual system will be necessary to get more accurate simulation results.