  We cope with a free boundary fluid-structure interaction model. In the model,
the viscous incompressible fluid interacts with elastic body via the common
boundary. The motion of the fluid is governed by Navier-Stokes equations while
the displacement of elastic structure is described by variable coefficient wave
equations. The dissipation is placed on the common boundary between fluid and
elastic body. Given small initial data, the global existence of the solutions
of this system is proved and the exponential decay of solutions are obtained.
