Linearization of a Coupled System of Nonlinear Elasticity and Viscous Fluid

Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic flow

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202514500079 ◽

2014 ◽

Vol 24 (09) ◽

pp. 1781-1822 ◽

Cited By ~ 10

Author(s):

G. P. Panasenko ◽

R. Stavre

Keyword(s):

Viscous Fluid ◽

Asymptotic Analysis ◽

Coupled System ◽

Thin Elastic Plate ◽

Periodic Flow ◽

Complete Asymptotic Expansion ◽

Thin Channel ◽

Elastic Wall ◽

Leading Term ◽

2D Elasticity

The first goal of this paper is to provide an asymptotic derivation and justification of the model studied in [Asymptotic analysis of a periodic flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. We consider the coupled system "viscous fluid flow–thin elastic plate" when the thickness of the plate, ε, tends to zero, while the density and the Young's modulus of the plate material are of order ε-1and ε-3, respectively. The plate lies on the fluid which occupies a thick domain. The complete asymptotic expansion is constructed when ε tends to zero and it is proved that the leading term of the expansion satisfies the equations of [Asymptotic analysis of a periodic flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. The second goal is the partial asymptotic decomposition formulation of the original problem when a part of the plate is described by a one-dimensional (1D) model while the other part is simulated by the two-dimensional (2D) elasticity equations. The appropriate junction conditions based on the previous asymptotic analysis are proposed at the interface point between the 1D and 2D equations. The error of the method is evaluated.

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Natural Frequencies of a Cracked Beam Coupled with a Compressible Sloshing Fluid

Shock and Vibration ◽

10.1155/2004/143536 ◽

2004 ◽

Vol 11 (3-4) ◽

pp. 505-519 ◽

Cited By ~ 2

Author(s):

Michele Di Sciuva ◽

Cecilia Surace

Keyword(s):

Boundary Condition ◽

Viscous Fluid ◽

Natural Frequencies ◽

Flexural Vibration ◽

Coupled System ◽

Cracked Beam ◽

Structure Interaction ◽

Linear Fracture ◽

Cantilevered Beam ◽

Interaction Problem

This article describes studies into the flexural vibration of a cracked cantilevered beam in contact with a non-viscous fluid. The crack has been represented by a mass-less rotational spring, the flexibility of which has been calculated using linear fracture mechanics. The coupled system is subject to undisturbed boundary condition at infinity in the fluid domain. A range of different boundary conditions have been analysed such as both incompressible and compressible fluid, with and without sloshing. Various crack sizes and positions have been considered in order to assess the effect of damage in the fluid-structure interaction problem.

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Weak Solutions to a Fluid-Structure Interaction Model of a Viscous Fluid with an Elastic Plate under Coulomb Friction Coupling

Mathematics ◽

10.3390/math9091026 ◽

2021 ◽

Vol 9 (9) ◽

pp. 1026

Author(s):

Reinhard Farwig ◽

Andreas Schmidt

Keyword(s):

Viscous Fluid ◽

Weak Solutions ◽

Coulomb Friction ◽

Local Existence ◽

Interaction Model ◽

Coupled System ◽

Three Dimensions ◽

Structure Interaction ◽

The Galerkin Method ◽

Upper Boundary

We consider the behavior of a viscous fluid within a container that has an elastic upper, free boundary. The movement of the upper boundary is described by a combination of a plate equation and a boundary condition of friction type that quantifies the elasticity of the boundary. We show the local existence of weak solutions to this coupled system in three dimensions, by applying the Galerkin method to a regularized version of the problem and using a fixed-point argument afterwards.

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