  In many occurrences of fluid-structure interaction time-periodic motions are
observed. We consider the interaction between a fluid driven by the three
dimensional Navier-Stokes equation and a two dimensional linearized elastic
Koiter shell situated at the boundary. The fluid-domain is a part of the
solution and as such changing in time periodically. On a steady part of the
boundary we allow for the physically relevant case of dynamic pressure boundary
values, prominent to model inflow/outflow. We provide the existence of at least
one weak time-periodic solution for given periodic external forces that are not
too large. For that we introduce new approximation techniques and a-priori
estimates.
