Longitudinal wave propagation in a multi-step rod with variable cross-section

Abstract

Vibration signals collected after propagation are usually different from the real ones of some vibration source due to the corresponding stop band of a particular propagation media. Here, the propagation characteristics of longitudinal wave are investigated when the signals pass through a multi-step rod with variable cross-section. Firstly, the transfer matrices for a single rod are derived based on the three wave theories, i.e. the elementary wave theory, the Love wave theory and the Mindlin-Herrmann wave theory, respectively. Next, the matching conditions for any two adjacent segments are analyzed, from which the transfer matrix for any step-rod with two or more segments are presented. Moreover, possible elastic constraint is also taken into consideration. Finally, several numerical examples for a step-rod with three segments are given by the present theoretical predictions and the finite element analysis, from which the performance of the three wave theories are compared with each other. The results show that the influences of the Poisson’s effect and shear deformation cannot be neglected, and the propagation characteristics of longitudinal wave in this multi-step rod may also be affected by the magnitude and location of the elastic constraint as well as the discontinuity of the cross-sections of adjacent segments.