The Band Gap Formation in Rotors With Longitudinal Periodicity and Quasi-Periodicity

Abstract

Modal spacing (band gaps) in the frequency spectrum of rotating machines can be imposed by geometric periodicity. By designing the rotor with a geometry that repeats periodically, we can impose to the vibration response of the rotor a modal “gap” considerably large, where no resonances appear. In this work, we consider that the rotating elements of the machine (e.g., the stages or the impellers) are the periodic elements of the rotor. In this disk-like configuration of the rotor, the system can present band gaps due to two different reasons: due to matching between the number of disks and the eigenmode wavenumber (usually in slender rotors)

due to the presence of local-mode shapes (usually in large rotors). Analytical modeling of the system is presented, whose approximated solution can be used to predict the start and stop frequencies of the band gaps. The limitations in band gap formation are also shown when the rotor is not perfectly periodic (quasi-periodic geometry). In this case, disk positioning plays an important role in the band gap formation.