Longitudinal wave propagation in a rod with variable cross-section

Abstract

Abstract 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.