  We address the system of partial differential equations modeling motion of an
elastic body interacting with an incompressible fluid. The fluid is modeled by
the incompressible Navier-Stokes equations while the structure is represented
by a damped wave equation $w_{tt}-\Delta w + \alpha w_t =0$, where $\alpha >0$.
We prove the global existence and exponential decay of strong solutions for
small initial data in a suitable Sobolev space. We show that the elastic
velocity $w_t$ and the acceleration $w_{tt}$ can be controlled by the $H^2$
elliptic estimates and by the dissipation of the fluid via the free interface.
We also find that, even though the vanishing of the final displacement $w$
appears invisible in the energy method, it can be deduced from the preservation
of total volume. Our approach allows for any superlinear perturbation of the
wave equation.
