Tikhonov well-posedness of the identification problem for fixing conditions for mechanical systems

The problem of the identification of fixing conditions is considered for distributed mechanical systems from three natural frequencies of their oscillations. Basing on the Plücker condition, which appears in the reconstruction of a matrix from its minors of maximal order, we construct the well-posedness set of the problem and prove its Tikhonov well-posedness. For a wide class of problems, we find an explicit solution to the identification problem for the matrix of boundary conditions written down in terms of the characteristic determinant of the corresponding spectral problem. We give examples of the solution of specific problems of mechanics and a counterexample showing that two natural frequencies are not enough for the uniqueness in the identification of the boundary conditions.