  We propose a model of ripples in suspended graphene sheets based on plate
equations that are made discrete with the periodicity of the honeycomb lattice
and then periodized. In addition, the equation for the displacements with
respect to the planar configuration contains a double-well site potential, a
nonlinear friction and a multiplicative white noise term satisfying the
fluctuation-dissipation theorem. The nonlinear friction terms agree with those
proposed by Eichler et al [Nature Nanotech. {\bf 6}, 339 (2011)] to explain
their experiments with a graphene resonator. The site double-well potential
indicates that the carbon atoms at each lattice point have equal probability to
move upward or downward off-plane. For the considered parameter values, the
relaxation time due to friction is much larger than the periods of membrane
vibrations and the noise is quite small. Then ripples with no preferred
orientation appear as long-lived metastable states for any temperature.
Numerical solutions confirm this picture.
