  We study the emergence of fluid flow in a closed chamber that is driven by
dynamical deformations of an elastic sheet. The sheet is compressed between the
sidewalls of the chamber and partitions it into two separate parts, each of
which is initially filled with an inviscid fluid. When fluid exchange is
allowed between the two compartments of the chamber, the sheet becomes
unstable, and its motion displaces the fluid from rest. We derive an analytical
model that accounts for the coupled, two-way, fluid-sheet interaction. We show
that the system depends on four dimensionless parameters: the normalized excess
length of the sheet compared to the lateral dimension of the chamber, $\Delta$;
the normalized vertical dimension of the chamber; the normalized initial volume
difference between the two parts of the chamber, $v_{\text{du}}(0)$; and the
structure-to-fluid mass ratio, $\lambda$. We investigate the dynamics at the
early times of the system's evolution and then at moderate times. We obtain the
growth rates and the frequency of vibrations around the second and the first
buckling modes, respectively. Analytical solutions are derived for these linear
stability characteristics within the limit of the small-amplitude
approximation. At moderate times, we investigate how the sheet escapes from the
second mode. Given the chamber's dimensions, we show that the initial energy of
the sheet is mostly converted into hydrodynamic energy of the fluid if
$\lambda\ll 1$, and into kinetic energy of the sheet if $\lambda\gg 1$. In both
cases most of the initial energy is released at time $ t_{\text{p}}\simeq \ln[c
\Delta^{1/2}/v_{\text{du}}(0)]/\sigma$, where $\sigma$ is the growth rate and
$c$ is a constant.
