Campbell diagrams of weakly anisotropic flexible rotors

Kirillov, Oleg (2009) Campbell diagrams of weakly anisotropic flexible rotors. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 465 (2109). pp. 2703-2723. ISSN 1364-5021

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Official URL: http://dx.doi.org/10.1098/rspa.2009.0055

Abstract

We consider an axi-symmetric flexible 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 eigenfrequencies at the nodes. The diagram is convenient for the analysis of the travelling waves in the rotating elastic continuum. Computing sensitivities of the doublets, we find that at every particular node the unfolding of the mesh into the branches of complex eigenvalues in the first approximation is generically determined by only four 2×2 sub-blocks of the perturbing matrix. 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’ and ‘viaduct’—which are sharply associated with the crossings of the unperturbed Campbell diagram with the definite symplectic (Krein) signature. The singularities connect the problems of wave propagation in the rotating continua with that of electromagnetic and acoustic wave propagation in non-rotating anisotropic chiral media. As mechanical examples a model of a rotating shaft with two degrees of freedom and a continuous model of a rotating circular string passing through the eyelet are studied in detail.

Item Type: Article
Uncontrolled Keywords: Campbell diagram, flexible rotor, dissipation-induced instabilities, subcritical flutter, symplectic (Krein) signature, non-Hermitian degeneracies
Subjects: F300 Physics
G100 Mathematics
H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Depositing User: Oleg Kirillov
Date Deposited: 23 Jan 2017 12:19
Last Modified: 23 Jan 2017 12:19
URI: http://nrl.northumbria.ac.uk/id/eprint/29286

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