Wave analysis of rotors with longitudinal periodicity

Abstract

The dynamics of rotating systems plays an important role in the efficiency and reliability of such machines. For this reason, understanding their dynamics is essential to predict and mitigate the resultant vibrations that can occur in such machines. Considering that vibration is essentially the propagation of waves in a continuous medium, methods of wave analysis can also be employed to investigate the dynamics of rotating systems, especially when the system presents some sort of periodicity. The difficulty lies in the fact that rotating systems are non-reciprocal systems due to the gyroscopic effects, which create forward and backward whirl motions with associated mode waves. The conventional wave methods usually do not tackle this problem. This work presents a methodology for analyzing rotating systems with wave methods based on the combination of conventional modal analysis, Bloch wave propagation theory, and directional frequency response functions. In this case, it is possible to separate the forward and backward modes, thus allowing the analysis of forward and backward wavenumbers separately. Consequently, one can draw separate dispersion diagrams for the wave modes associated with the forward and backward motions of the rotor. The numerical results show the feasibility of the method, and the methodology is applied experimentally to a rotating system in the laboratory.