  We present results for time-dependent electron transport in a ballistic
graphene field-effect transistor with an ac-driven gate. Nonlinear response to
the ac drive is derived utilizing Floquet theory for scattering states in
combination with Landauer-B\"uttiker theory for transport. We identify two
regimes that can be useful for applications: (i) low and (ii) high doping of
graphene under source and drain contacts, relative to the doping level in the
graphene channel, which in an experiment can be varied by a back gate. In both
regimes, inelastic scattering induced by the ac drive can excite quasi-bound
states in the channel that leads to resonance promotion of higher order
sidebands. Already for weak to intermediate ac drive strength, this leads to a
substantial change in the direct current between source and drain. For strong
ac drive with frequency $\Omega$, we compute the higher harmonics of
frequencies $n\Omega$ ($n$ integer) in the source-drain conductance. In regime
(ii), we show that particular harmonics (for instance $n=6$) can be selectively
enhanced by tuning the doping level in the channel or by tuning the drive
strength. We propose that the device operated in the weak-drive regime can be
used to detect THz radiation, while in the strong-drive regime it can be used
as a frequency multiplier.
