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Interactions of an elastic solid with a viscous fluid: Eigenmode analysis. (English) Zbl 0757.76028

Summary: We study the interaction of a viscous fluid with an elastic solid. Of particular interest are the eigenmodes of the coupled system. Starting from the Navier-Stokes equations for the fluid and the linear elasticity equations for the solid, we derive the linear equations governing the motion of the system. It is shown how a variational formulation of the problem may be obtained by re-scaling the displacement unknowns. The finite-element technique is then used to discretize the equations. The resulting quadratic eigenvalue problem is solved by means of an inverse iteration procedure.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
74B10 Linear elasticity with initial stresses
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References:

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