On a Fluid-Structure Model in Which the Dynamics of the Structure Involves the Shear Stress Due to the Fluid |
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Authors: | Marié Grobbelaar-Van Dalsen |
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Institution: | (1) Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, Republic of South Africa |
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Abstract: | In this paper we consider a model for fluid-structure interaction. The hybrid system describes the interaction between an
incompressible fluid in a three-dimensional container with interior a fixed domain and a thin elastic plate, the interface,
which coincides with a flexible flat part of the surface of the vessel containing the fluid. The motion of the fluid is described
by the linearized Navier–Stokes equations and the deformation of the plate by the classical plate equations for in-plane motions,
modified to include the viscous shear stress which the fluid exerts on the plate as well as damping of Kelvin–Voigt type.
We establish the existence of a unique weak solution of the interactive system of partial differential equations by considering
an appropriate variational formulation. Uniform stability of the energy associated with the model is shown under the assumption
that the potential plate energy is dominated by the dissipation induced by the viscosity of the fluid. The retention of the
physical parameters in the problem is an a priori requirement in this physical condition.
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Keywords: | " target="_blank"> Fluid-structure interaction structural acoustic model viscous fluid shear stress Navier– Stokes equations quasi-longitudinal waves plate equations weak solution uniform stability |
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