Asymptotics of eigenvalues of the elasticity theory problem with the Winkler–Steklov spectral conditions at small parts of the boundary

Asymptotics of eigenpairs of the elasticity theory system is constructed in a three-dimensional domain with the Winkler–Steklov spectral boundry conditions at several small parts (the contact blots) and the Neumann (traction-free) conditions at the remaining part of the boundary. The asymptotic structures are essentially dependent on the distribution of the blots and the elastic or springy type of the contact. Various examples are considered and open questions are formulated.