Averaging of eigenvalues and eigenfunctions of a boundary value problem of elasticity theory in a perforated domain

For a system of the theory of elasticity with rapidly oscillating periodic coefficients of period $\varepsilon$, a boundary value problem is considered in a perforated domain with a periodic structure of period $\varepsilon$. An estimate is derived for the deviation of the eigenvalues and eigenfunctions of this problem from those of the corresponding homogenized problem. The character of the dependence of the deviation on the small parameter $\varepsilon$ is given.