中心刚体-楔形梁-质点刚柔耦合系统动力学分析

Dynamics analysis of the hub and tapered beam coupled system with tip mass

研究了中心刚体-楔形梁-质点系统的固有特性和动力学响应。楔形梁为Euler-Bernoulli梁,高度和宽度都沿着梁的长度方向线性变化。利用广义Hamilton原理和一阶近似耦合模型得到了含有楔形梁完全耦合且时变的微分/代数控制方程。考虑了离心刚化效应,利用有限元得到了系统完全耦合的有限维方程。忽略轴向与横向位移的相互作用,得到了系统的一致质量、阻尼和刚度矩阵。最后对楔形梁和等截面梁在有无端部质点的四种结构进行仿真,结果表明存在显著差异,重点比较了同等条件下楔形梁与等截面梁的差异指数,说明均匀梁和楔形梁的截面细微的差别能够导致系统频率和动力学响应的明显差别。指出实际系统中使用楔形梁模型能够得到更为精确的仿真结果。

The intrinsic characteristics and the flexible motion of tapered Euler-Bernoulli beam with tip mass and a rotating hub are investigated. The breadth and the depth of the tapered beam vary linearly along its length. Integration-differential governing equations are derived from the extended Hamilton principle and the first-order approximation coupling model. The governing equations, describing rigid-flexible and axial-transverse coupled action, are not only fully coupled equations, but also time dependent, which can be used to simulate the high-speed mechanisms because the centrifugal stiffening effect has been taken into account. Simplifying the above coupled equations and using the finite element method, the finite dimension dynamics formulation is obtained. Meanwhile, the damp, stiffness and mass matrices of the system are derived. The numerical simulations of the four kinds of structures are present to show the differences in dynamics response. By comparing the uniform and the tapered system in the same condition, the obtained results indicate that a little difference in section can cause significant difference in natural frequencies and dynamics response. To gain more accurate results, it is necessary to use the tapered beam in the practical system.