  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 eigenfrequencies
at the nodes. The diagram is convenient for the analysis of the traveling waves
in the rotating elastic continuum. Computing sensitivities of the doublets we
find that at every particular node the untwisting of the mesh into the branches
of complex eigenvalues in the first approximation is generically determined by
only four 2x2 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 associated with the
crossings of the unperturbed Campbell diagram with the definite 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.
