  We study the dynamic structure factor of fluctuating elastic thin sheets
subject to conservative (athermal) random forcing. In Steinbock, Katzav &
Boudaoud, Phys. Rev. Research 4, 033096 (2022), the static structure factor of
such a sheet was studied. In this paper, we recap the model developed there and
investigate its dynamic properties. Using the self-consistent expansion (SCE),
the time dependent two-point function of the height profile is determined and
found to decay exponentially in time. Despite strong nonlinear coupling, the
decay rate of the dynamic structure factor is found to coincide with the
effective coupling constant for the static properties which suggests that the
model under investigation exhibits certain quasi-linear behaviour. Confirmation
of these results by numerical simulations is also presented.
