  Natural and resonant oscillations of suspended circular graphene and
hexagonal boron nitride (h-BN) membranes (single-layer sheets lying on a flat
substrate having a circular hole of radius $R$) have been simulated using
full-atomic models. Substrates formed by flat surfaces of graphite and h-BN
crystal, hexagonal ice, silicon carbide 6H-SiC and nickel surface (111) have
been used. The presence of the substrate leads to the forming of a gap at the
bottom of the frequency spectrum of transversal vibrations of the sheet. The
frequencies of natural oscillations of the membrane (oscillations localized on
the suspended section of the sheet) always lie in this gap, and the frequencies
of oscillations decrease by increasing radius of the membrane as $(R+R_i)^{-2}$
with nonezero effective increase of radius $R_i>0$. The modeling of the sheet
dynamics has shown that small periodic transversal displacements of the
substrate lead to resonant vibrations of the membranes at frequencies close to
eigenfrequencies of nodeless vibrations of membranes with a circular symmetry.
The energy distribution of resonant vibrations of the membrane has a circular
symmetry and several nodal circles, whose number $i$ coincides with the number
of the resonant frequency. The frequencies of the resonances decrease by
increasing the radius of the membrane as $(R+R_i)^{\alpha_i}$ with exponent
$\alpha_i<2$. The lower rate of resonance frequency decrease is caused by the
anharmonicity of membrane vibrations.
