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In this paper, we study a nonlinear fluid-structure interaction problembetween a viscoelastic beam and a compressible viscous fluid. The beam isimmersed in the fluid which fills a two-dimensional rectangular domain withperiodic boundary conditions. Under the effect of periodic forces acting on thebeam and the fluid, at least one time-periodic weak solution is constructedwhich has a bounded energy and a fixed prescribed mass.

On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams