轴向运动二维传输结构动力学有限元建模与仿真

基于物理中面概念和经典薄板理论，应用有限元法研究了机械工程中的二维传输结构作轴向运动时的面外自由振动特性．根据实际工程结构特点及设计要点，考虑受双向预张应力作用的传输薄板结构模型，由哈密顿原理出发严格导出了结构的有限元动力学方程，得到了体现轴向传输结构特性的陀螺矩阵．该矩阵具有反对称结构，这与加权余量法所得的陀螺矩阵结构不同．采用3 节点三角形单元离散求解域，且单元不受轴向运动影响，给出了单元密度对计算结果精度的影响．分析了传输结构预张应力和轴向速度与自由振动固有频率的关系；考察了不同结构的陀螺矩阵对数值结果的影响．将部分结果与ANSYS 软件模拟对比，显示出良好的一致性，证明了本文方法的有效性．研究结果可为典型传输带等结构的振动控制提供参考，建模方法可为ANSYS等计算软件添加轴向运动结构新模块提供理论依据．

Finite Element Modeling and Simulation of Dynamics of Two-Dimensional Transmission Structures with Axial Motion

Based on the concept of physical middle plane and the theory of classical thin plate, the out-of-plane free vibration of two-dimensional transmission structures with axial motion is investigated using the finite element method (FEM). Considering structural characteristics and design requirements in practical engineering, a structural model of transmission thin plates subjected to biaxial pre-tension is developed to strictly derive the finite element dynamic equations based on Hamilton’s principle. A gyroscope matrix reflecting the characteristics of transmission structures is obtained. The matrix has an anti-symmetric structure, which is different from the gyroscope matrix determined by the weighted residual method. The 3-node triangular element is employed to discretize the problem domain, and the element is not affected by the axial motion. The influence of element density on the calculation accuracy is studied. The effects of the pre-tension and the axial velocity on the natural frequencies of the transmission structures are analyzed. The influence of gyroscope matrices with different structures on the numerical results is examined. Some results are compared with those by ANSYS software with a good consistency, which validates the presented model. The research could provide reference for the vibration control of typical transmission structures. The modeling method can provide a theoretical basis for adding a new module of axially moving structures to commercial calculation software such as ANSYS.