Kirchhoff plate with the Winkler–Steklov conditions at small parts of the edge

Asymptotics is constructed for eigenvalues and eigenfunctions of the biharmonic equation with the Neumann conditions perturbed by the spectral Winkler–Steklov conditions at small parts of the plate’s edge. The zero eigenvalue has multiplicity three and the corresponding eigenfunctions are linear. Asymptotic expansions of positive eigenvalues differ essentially in the mid- and high-frequency ranges of the spectrum. In particular, eigenfunctions at low and medium frequencies are distributed along the entire domain while eigenfunctions at high frequencies are concentrated in the vicinity of the edge perturbations.