  We consider the triharmonic operator subject to homogeneous boundary
conditions of intermediate type on a bounded domain of the N-dimensional
Euclidean space. We study its spectral behaviour when the boundary of the
domain undergoes a perturbation of oscillatory type. We identify the
appropriate limit problems which depend on whether the strength of the
oscillation is above or below a critical threshold. We analyse in detail the
critical case which provides a typical homogenization problem leading to a
strange boundary term in the limit problem.
