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 引用本文: 刘星光, 唐有绮, 周远. 三种典型轴向运动结构的振动特性对比[J]. 力学学报, 2020, 52(2): 522-532.
Liu Xingguang, Tang Youqi, Zhou Yuan. COMPARISON OF VIBRATION CHARACTERISTICS OF THREE TYPICAL AXIALLY MOVING STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 522-532.
 Citation: Liu Xingguang, Tang Youqi, Zhou Yuan. COMPARISON OF VIBRATION CHARACTERISTICS OF THREE TYPICAL AXIALLY MOVING STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 522-532.

## COMPARISON OF VIBRATION CHARACTERISTICS OF THREE TYPICAL AXIALLY MOVING STRUCTURES

• 摘要: 轴向运动结构的横向振动一直是动力学领域的研究热点之一.目前大多数的文献只涉及对一种模型的研究,而针对几种模型的对比分析较少.本文对3种典型轴向运动结构(Euler梁、窄板和对边简支对边自由的板)的振动特性进行了对比分析.针对工程中不同的结构参数,本文为其理论研究中选择更加合理的模型提供了参考.通过复模态方法求解了3种模型的控制方程,给出了其相应的固有频率及模态函数.对于板模型,同时考虑了其自由边界的两种刚体位移以及弯扭耦合振动3种情况.通过数值算例给出了3种模型的前四阶固有频率随轴速和长宽比的变化情况,并应用微分求积法对复模态方法得到的解析解进行验证.特别采用三维图的形式分析了不同的轴速、阻尼、刚度和长宽比等参数混合时对3种模型第一阶固有频率的影响,着重研究了窄板和梁的不同的长宽比和轴速混合时对两者的第一阶固有频率的相对误差的影响.结果表明：随着轴速的增大,3种模型的固有频率逐渐减小. 窄板是板的一种简化模型.在各参数值发生变化时,阻尼对第一阶固有频率的影响最小.长宽比很大,轴速很小或为零时,复杂模型可以简化为简单模型.

Abstract: The transverse vibration of the axially moving structure is always one of the hot topics in the field of dynamics. At present, most literatures are considering the study of one model. There are few researches considering the comparative analysis of several models. The vibration characteristics of three typical axially moving structures, such as the Euler beam, the panel, and the plate with two opposite sides simply supported and other two free, are compared and analyzed in this paper. In view of different structural parameters in engineering, this paper provides a reference for choosing a more reasonable model in the study of vibration theory. The governing equations of the three models are solved by the complex mode method. The corresponding natural frequencies and mode functions can be obtained. For the plate model, two rigid displacements and the coupled flexural and torsional vibration are both considered. The variations of the first four order natural frequencies of the three models with the axial velocity and the aspect ratio are given by numerical examples. At the same time, the analytical solution obtained by the complex modal method is verified by the differential quadrature method. The influence of different axial speed, damping, stiffness, and aspect ratio on the first order natural frequency of three models is analyzed by adopting the form of three-dimensional diagram for the first time. The effects of different aspect ratios and axial speed mixing on the relative errors of the first natural frequencies the first order natural frequency of the plates and beams are emphatically studied. The results show that the natural frequency of the three structures decreases gradually with the increasing axially speed. The panel is a simplified model of the plate. The damping has the least effect on the first order natural frequency when other parameters change. The complex model can be simplified into a simple model when the moving structure has a large aspect ratio and a small axial speed.

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