  Mechanical dissipation poses an ubiquitous challenge to the performance of
nanomechanical devices. Here we analyze the support-induced dissipation of
high-stress nanomechanical resonators. We develop a model for this loss
mechanism and test it on silicon nitride membranes with circular and square
geometries. The measured Q-values of different harmonics present a
non-monotonic behavior which is successfully explained. For azimuthal harmonics
of the circular geometry we predict that destructive interference of the
radiated waves leads to an exponential suppression of the clamping loss in the
harmonic index. Our model can also be applied to graphene drums under high
tension.
