Longitudinal wave propagation in a rod with variable cross-section
Longitudinal wave propagation in a rod with variable cross-section
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DOI：
10.1016/j.jsv.2013.09.010
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发表时间：
2014-01
影响因子：
4.7
通讯作者：
C. Gan;Yimin Wei;Shixi Yang
中科院分区：
文献类型：
--
作者：
C. Gan;Yimin Wei;Shixi Yang
机械状态监测需要振动数据，在许多工程应用中，振动数据只能通过杆、壳、旋转轴或其他部件传输后间接收集。研究这些部件的振动传递特性对于保证间接收集数据的效率非常有帮助。在这里，研究了变截面杆中的纵波传播。首先，根据基本波动理论、洛夫理论和明德林-赫尔曼理论建立了杆的运动方程。其次，采用传递矩阵方法从推导的运动方程探索杆的传播特性。最后，利用两种截面呈指数形式和多项式形式变化的杆件来说明纵波传播特性的解析预测，并与有限元分析（FEA）方法的结果进行比较。结果表明，泊松效应或剪切变形对杆中的纵波传播起着非常重要的作用，并且可以适度加宽杆的阻带。此外，即使考虑了泊松效应或剪切变形，杆的截止频率与横截面的变化形式无关，而是取决于杆两端之间的面积比。
Vibration data are required for condition monitoring in machinery, and can only be collected indirectly after transferring through rods, shells, rotating shafts or other components in many engineering applications. Investigation on the transfer characteristics of vibration in these components is very helpful to guarantee the efficiency of the data collected indirectly. Here, the longitudinal wave propagation in a rod with variable cross-section is investigated. First, the equations of motion are established for the rod based upon the elementary wave theory, the Love theory and the Mindlin–Herrmann theory. Second, the transfer matrix method is employed to explore the propagation characteristics of the rod from the derived equations of motion. Finally, two kinds of rods with the cross-sections varying in the exponential and the polynomial forms are used to illustrate the analytical predictions of the propagation characteristics of the longitudinal wave, which are compared with the results from the finite element analysis (FEA) method. It is shown that Poisson's effect or the shear deformation plays a very important role in the longitudinal wave propagation in the rod and can widen the rod's stop band moderately. Moreover, the cut-off frequency of the rod is unconcerned with the variation form of the cross-section, but dependent on the area ratio between both the ends of the rod, even though Poisson's effect or shear deformation is included.