Stability analysis of rotating beams rubbing on an elastic circular structure

TL;DR

This paper analyzes the stability of a system with rotating beams on an elastic ring, considering various dynamic phenomena and the effects of rubbing, using the Routh-Hurwitz criterion within a rotating frame.

Contribution

It develops a comprehensive stability model for rotating beams on an elastic ring, including effects of in-plane deformations, rubbing, and beam orientation, using an energy approach and stability criteria.

Findings

Rubbing induces immediate instability at any non-zero rotational speed.

Mode couplings and divergence instabilities are identified in the system.

The angle between beams and the ring affects the system's stability and frequency response.

Abstract

This paper presents the stability analysis of a system composed of rotating beams on a flexible, circular fixed ring, using the Routh-Hurwitz criterion. The model displayed has been fully developed within the rotating frame by use of an energy approach. The beams considered possess two degrees of freedom (dofs), a flexural motion as well as a traction/compression motion. In-plane deformations of the ring will be considered. Divergences and mode couplings have thus been underscored within the rotating frame and in order to simplify understanding of all these phenomena, the dofs of the beams will first be treated separately and then together. The dynamics of radial rotating loads on an elastic ring can create divergence instabilities as well as post-critical mode couplings. Moreover, the flexural motion of beam rubbing on the ring can also lead to mode couplings and to the locus-veering phenomenon. The presence of rubbing seems to make the system unstable as soon as the rotational speed of the beams is greater than zero. Lastly, the influence of an angle between the beams and the normal to the ring's inner surface will be studied with respect to system stability, thus highlighting a shift frequency phenomenon.