We calculate the vibrational density-of-states in an insulating nanoparticlethat is in weak mechanical contact with a semi-infinite substrate. The work ismotivated by a recent experiment by Yang et al., where the low-energy phonondensity-of-states of Y2O3 nanoparticles doped with Eu was measured. Preliminaryresults presented here, based on the conventional quasiparticle-poleapproximation for the phonon propagator, are in reasonable agreement withexperiment.
