  We present a study of resonant vibrational coupling between adsorbates and an
elastic substrate at low macroscopic coverages. In the first part of the paper
we consider the situation when adsorbates form aggregates with high local
coverage. Based upon our previously published theory, we derive formulas
describing the damping rate of adsorbate vibrations for two cases of such
aggregation: (i) adsorbates attached to step edges and (ii) adsorbates forming
two-dimensional islands. We have shown that damping is governed by local
coverage. Particularly, for a wide range of resonant frequencies, the damping
rate of adsorbates forming well separated islands is described by the damping
rate formula for a periodic overlayer with the coverage equal to the local
coverage in the island. The second part of the paper is devoted to facilitating
the evaluation of damping rates for a disordered overlayer. The formula
describing the damping rate involves the parameter $\beta$ which is related to
the local density of phonon states at the substrate surface and does not allow
a closed-form representation. For substrates of isotropic and cubic symmetries,
we have developed a good analytical approximation to this parameter. For a vast
majority of cubic substrates the difference between the analytical
approximation and numerical calculation does not exceed 4%.
