A Study on the Wave Characteristics of the Periodic Structures for the Vibration Attenuation in a Rotating Ring

Abstract

In this work, the wave characteristics are studied on the periodic structure attenuating the vibration in a rotating ring, which is often the main power transmission element of many machines. The rotating ring structure is modeled as an arc-shaped Euler-Bernoulli beam, on which the periodic structures in the form of stiffeners are distributed. The propagation constant of the wave is obtained by solving the eigenvalue problem, utilizing the transfer matrix method and Floquet's theorem. When the stiffeners are periodically attached along the ring, the stopbands of flexural or longitudinal wave propagation appear at the resonance frequencies of a unit cell in a periodic arrangement. In the case of circular rings, flexural and longitudinal waves are coupled at some narrow frequency bands, which produces additional stopbands. When it comes to a rotating ring, the wave propagation characteristics depend on the forward or backward directions because of the Coriolis force. This effect causes asymmetric stopbands for the forward and backwards waves. Such a characteristic helps increase the bandwidth of the stopbands of the propagating structural waves due to the excitation on the rotating ring with periodic structures.