  We theoretically analyse the dynamics of a suspended graphene membrane which
is in tunnel contact with grounded metallic electrodes and subjected to
ac-electrostatic potential induced by a gate electrode. It is shown that for
such system the retardation effects in the electronic subsystem generate an
effective pumping for the relatively slow mechanical vibrations if the driving
frequency exceeds the inverse charge relax- ation time. Under this condition
there is a critical value of the driving voltage ampli- tude above which the
pumping overcomes the intrinsic damping of the mechanical resonator leading to
a mechanical instability. This nonresonant instability is saturated by
nonlinear damping and the system exhibits self-sustained oscillations of
relatively large amplitude.
