  We study the spectral behavior of higher order elliptic operators upon domain
perturbation. We prove general spectral stability results for Dirichlet,
Neumann and intermediate boundary conditions. Moreover, we consider the case of
the bi-harmonic operator with those intermediate boundary conditions which
appears in study of hinged plates. In this case, we analyze the spectral
behavior when the boundary of the domain is subject to a periodic oscillatory
perturbation. We will show that there is a critical oscillatory behavior and
the limit problem depends on whether we are above, below or just sitting on
this critical value. In particular, in the critical case we identify the
strange term appearing in the limiting boundary conditions by using the
unfolding method from homogenization theory.
