Perturbation of eigenvalues in multiparameter families of non-self-adjoint operator matrices
We consider two-point non-self-adjoint boundary eigenvalue problems for linear
matrix differential operators. The coefficient matrices in the differential
expressions and the matrix boundary conditions are assumed to depend analytically
on the complex spectral parameter and on the vector of real physical
parameters p. We study perturbations of semi-simple multiple eigenvalues
as well as perturbations of non-derogatory
eigenvalues under small variations of p. Explicit formulae describing the
bifurcation of the eigenvalues are derived.
Application to the problem of excitation of unstable modes in rotating elastic continua revealed that
selection of the unstable modes 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.