The influence of transverse cracks to propagation characteristics of elastic waves propagating in a non-uniform shaft

Abstract

The propagation mechanism of vibration in a media such as a non-uniform rotating shaft is an important topic since it can help to control the vibration of the media, or to reduce the noise. Vibration propagates in a non-uniform rotating shaft in the form of elastic waves and the propagation characteristics of the waves are affected by the non-uniform factors, the transverse cracks and the rotating speed, etc. This study deals with the propagation characteristics of the elastic waves in a non-uniform shaft with transverse cracks by adopting the Transfer Matrix method. First, the transfer matrix for a single non-uniform shaft is derived by constructing the motion equations derived with Equilibrium Equations. Second, the transfer matrix for a transverse crack is studied. Crack Mode III is adopted, and the transverse crack is modeled as a local spring, the local flexibility coefficient of which is deduced. The transfer matrix for the non-uniform shaft with transverse cracks is then derived by combining the individual matrixes. Finally, several numerical examples are used to illustrate the influence of different crack depths and alternative rotating speeds on the propagation characteristics of the elastic waves, which are compared with the results from the experimental analyses. It's shown that a new stop band will come out at lower frequency region when a transverse crack occurs and the bandwidth of which will be wider and wider as the increase of the depth of the crack, and the rotating speed mainly affects the first stop band, the central frequency of which will decrease as the increase of the rotating speed.