Singular features of traveling wave propagation in rotating elastic bodies of revolution in frictional contact

Oleg N. Kirillov*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Electromagnetic and acoustic wave propagation in the stationary anisotropic media, such as optically anisotropic crystals that are both absorbing and chiral, is accompanied by the polarization singularities among which the singular axes are the most prominent [8, 11]. These are degeneracies where the two refractive indices are equal and that for a transparent non-chiral crystal condense pairwise onto the optic axes. The present work reveals these singularities in case of the traveling bending waves that propagate in the rotating continua. We consider an axi-symmetric rotor perturbed by dissipative, conservative, and non-conservative positional forces originated at the contact with the anisotropic stator. The Campbell diagram of the unperturbed system is a mesh-like structure in the frequency-speed plane with double ei-genfrequencies at the nodes. Computing sensitivities of the doublets we find that selection of the unstable modes that cause self-excited vibrations in the subcritical speed range is governed by the exceptional points at the corners of the singular eigenvalue surfaces - "double coffee filter" [12] and "viaduct" - that are sharply associated with the crossings of the unperturbed Campbell diagram with the definite Krein signature. As a mechanical example a rotating circular string passing through the eyelet is studied in detail.

Original languageEnglish
Title of host publication16th International Congress on Sound and Vibration 2009, ICSV 2009
Pages1245-1252
Number of pages8
Volume2
Publication statusPublished - 2009
Externally publishedYes
Event16th International Congress on Sound and Vibration 2009, ICSV 2009 - Krakow, Poland
Duration: 5 Jul 20099 Jul 2009

Conference

Conference16th International Congress on Sound and Vibration 2009, ICSV 2009
CountryPoland
CityKrakow
Period5/07/099/07/09

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