文档介绍：ARTICLE IN1 PRESS
JOURNAL OF
SOUND AND
VIBRATION
Journal of Sound and Vibration 299 (2007) 1005–1032
ate/jsvi
Stability analysis of rotating beams rubbing on an
elastic circular structure
N. LesaffreÃ, J.-J. Sinou, F. Thouverez
Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Syste`mes, RS 5513, Equipe Dynamique des Syste`mes
et des Structures, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France
Received 12 April 2006; received in revised form 4 July 2006; accepted 7 August 2006
Available online 12 October 2006
Abstract
This paper presents the stability analysis of a posed 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 pression
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.
r 2006 Elsevier Ltd. All rights reserved.
1. Introduction
Problems caused by loads moving over elastic structures occur rather frequently. The case of rotating
structures has been given special attention. A flexi