  We consider the homogenization of a singularly perturbed self-adjoint fourth
order elliptic equation with locally periodic coefficients, stated in a bounded
domain. We impose Dirichlet boundary conditions on the boundary of the domain.
The presence of large parameters in the lower order terms and the dependence of
the coefficients on the slow variable give rise to the effect of localization
of the eigenfunctions. We show that the $j$th eigenfunction can be approximated
by a rescaled function that is constructed in terms of the $j$th eigenfunction
of fourth or second order order effective operators with constant coefficients,
depending on the large parameters.
