In this paper, the models of Euler–Bernoulli beams on the Winkler foundations are considered.
The novelty of the research is in consideration of the models with an arbitrary variable coefficient
of foundation. Qualitative results that influence the symmetry of the coefficient of foundation on the
spectral properties of the corresponding problems are obtained, for which specific variable coefficients
of foundation are tested using numerical calculations. Three types of fixing at the ends are studied:
clamped-clamped, hinged-hinged and free-free. The conditions of the stiffness and types of beam
fixing have been found for the set of eigenvalues of boundary value problems on a full segment
and can be represented as two groups of the eigenvalues of certain problems on a half segment.
Such qualitative spectral properties of a mechanical system can contribute to the creation of various
algorithms for nondestructive testing, which are widely used in technical acoustics.
