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

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.