Asymptotic analysis of a thin fluid layer-elastic plate interaction problem

ABSTRACT

We study the nonstationary flow of an incompressible fluid in a thin rectangle with an elastic plate as the upper part of the boundary. The flow is governed by a time-dependent pressure drop and an external force and it is modeled by Stokes equations. The dynamic of this fluid–structure interaction problem is studied in the limit when the thickness of the fluid domain tends to zero. Using the asymptotic techniques, we obtain for the effective plate displacement a sixth-order parabolic equation with a non standard boundary conditions. Results on existence, uniqueness and regularity of the solution are proved. The approximation is justified through a weak convergence theorem.

KEYWORDS:

• Fluid-structure interaction
• Stokes equations
• elastic plate
• asymptotic analysis

AMS SUBJECT CLASSIFICATIONS:

• 74F10
• 35Q30
• 76M45

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Croatian Science Foundation [grant number 3955]. Mathematical modeling and numerical simulations of processes in thin or porous domains.