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Matthieu Hillairet - One of the best experts on this subject based on the ideXlab platform.

  • On an existence theory for a Fluid-beam problem encompassing possible contacts
    2019
    Co-Authors: Jean-jérôme Casanova, Celine Grandmont, Matthieu Hillairet
    Abstract:

    In this paper we consider a coupled system of pdes modelling the interaction between a two-dimensional incompressible viscous Fluid and a one-dimensional elastic beam located on the upper part of the Fluid domain boundary. We design a functional framework to define weak solutions in case of contact between the elastic beam and the bottom of the Fluid Cavity. We then prove that such solutions exist globally in time regardless a possible contact by approximating the beam equation by a damped beam and letting this additional viscosity vanishes.

  • Existence of Global Strong Solutions to a Beam–Fluid Interaction System
    Archive for Rational Mechanics and Analysis, 2016
    Co-Authors: Celine Grandmont, Matthieu Hillairet
    Abstract:

    We study an unsteady nonlinear Fluid–structure interaction problem which is a simplified model to describe blood flow through viscoelastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier–Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The Fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the Fluid–structure interface and the action–reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain, in particular that contact between the viscoelastic wall and the bottom of the Fluid Cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, and of the existence of strong solutions globally in time, in the frame of interactions between a viscous Fluid and a deformable structure.

  • Existence of global strong solutions to a beam-Fluid interaction system
    Archive for Rational Mechanics and Analysis, 2016
    Co-Authors: Celine Grandmont, Matthieu Hillairet
    Abstract:

    We study an unsteady non linear Fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The Fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the Fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the Fluid Cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous Fluid and a deformable structure.

Mohamed Haddar - One of the best experts on this subject based on the ideXlab platform.

  • Vibro-acoustic analysis of laminated double glazing using the force identification method
    Journal of Theoretical and Applied Mechanics, 2014
    Co-Authors: Mounir Ben Jdidia, Ali Akrout, Dhouha Tounsi, Tahar Fakhfakh, Mohamed Haddar
    Abstract:

    This paper presents a procedure for identifying wave forms and excitation frequencies of some forces applied on a given complex Fluid-structure coupled system by using only its vibro-acoustic response. The considered concept is called the Independent Component Analysis (ICA) which is based on the Blind Source Separation (BSS). In this work, the ICA method is exploited in order to determine the excitation force applied to a thin-film laminated double glazing system enclosing a thin Fluid Cavity and limited by an elastic joint. The dynamic response of the studied Fluid-structure coupled system is determined by finite element discretization and minimization of the homogenized energy functional of the coupled problem. This response will serve as the input for the ICA algorithm in order to extract the applied excitation.

  • Vibro-acoustic behaviour of laminated double glazing enclosing a viscothermal Fluid Cavity
    Applied Acoustics, 2009
    Co-Authors: Ali Akrout, Lotfi Hammami, Mabrouk Ben Tahar, Mohamed Haddar
    Abstract:

    Abstract This paper presents a new numerical model to investigate the vibro-acoustic behaviour of two laminated glass plates enclosing a thin viscothermal Fluid Cavity. The aim of this work is to develop an original five layer (two skins plies, two adhesive films and a core ply) laminated plate finite element by mixing Kirchhoff and Mindlin plate’s theory. The formulation is based on the theory that accounts for the transverse shear in the adhesive films and in the core. The acousto-elastic model is established in dimensionless appropriate form including the effects of viscosity and thermal conductivity of Fluid and by taking into account the Fluid-structure interaction. The discretization of the energy functional by finite element method gives after minimisation a symmetrical coupled matrix system in which the acoustic matrices are frequency dependent. Therefore, an iterative procedure is derived to determine the eigenmodes of the coupled system. The modal approach is adopted to determine the vibro-acoustic system’s response. Then, the validation of the new laminate finite element model is achieved by comparing the sandwich plate results against data obtained from literature. Subsequently, predicted responses, such as the vibration transmissibility and the transmission loss of the coupled system, for a given laminated double glazing under an imposed homogeneous pressure are presented and discussed. Numerical results show the importance of both lamination and viscothermal Fluid effects on double glazing vibro-acoustic behaviour.

  • Viscothermal Fluid effects on vibro-acoustic behaviour of double elastic panels
    International Journal of Mechanical Sciences, 2008
    Co-Authors: Ali Akrout, Lotfi Hammami, Chafik Karra, Mohamed Haddar
    Abstract:

    Abstract This paper deals with the vibro-acoustic behaviour of two vibrating plates coupled to a viscothermal Fluid Cavity. The acousto-elastic model is established in dimensionless appropriate form including the effects of viscosity and thermal conductivity of Fluid and taking into account the Fluid–structure interaction. The finite element method is used for the discretization of the functional of energy, which gives after minimization a symmetrical coupled matrix system in which the acoustic matrices are frequency dependent. For this purpose, an iterative procedure is derived to determine the eigenmodes of the coupled system. The modal approach is adopted to determine the vibro-acoustic system's response which the numerical results show the importance of the viscothermal effects in the case of thin Fluid layers.

  • Simulation of Viscothermal Losses on the Acoustic Behaviour of a Thin Fluid Layer Enclosed Between Two Oscillating Plates
    Building Acoustics, 2006
    Co-Authors: Chafik Karra, Ali Akrout, Lotfi Hammami, Mohamed Haddar
    Abstract:

    This article deals with a theoretical investigation for the analysis of a double-plate system enclosing a viscothermal Fluid Cavity. Dynamic equations of the coupled system are established in appropriate dimensionless form including the effects of viscosity and thermal conductivity of the Fluid. The pressure wave equation is derived in in-plane form. This equation is solved analytically in the case of oscillating plate motions in order to determine the acoustic pressure in the Cavity. Numerical results are presented for the case of two modal shapes. They show the importance of the viscothermal effects in the case of thin Fluid layers.

Celine Grandmont - One of the best experts on this subject based on the ideXlab platform.

  • On an existence theory for a Fluid-beam problem encompassing possible contacts
    2019
    Co-Authors: Jean-jérôme Casanova, Celine Grandmont, Matthieu Hillairet
    Abstract:

    In this paper we consider a coupled system of pdes modelling the interaction between a two-dimensional incompressible viscous Fluid and a one-dimensional elastic beam located on the upper part of the Fluid domain boundary. We design a functional framework to define weak solutions in case of contact between the elastic beam and the bottom of the Fluid Cavity. We then prove that such solutions exist globally in time regardless a possible contact by approximating the beam equation by a damped beam and letting this additional viscosity vanishes.

  • Existence of Global Strong Solutions to a Beam–Fluid Interaction System
    Archive for Rational Mechanics and Analysis, 2016
    Co-Authors: Celine Grandmont, Matthieu Hillairet
    Abstract:

    We study an unsteady nonlinear Fluid–structure interaction problem which is a simplified model to describe blood flow through viscoelastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier–Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The Fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the Fluid–structure interface and the action–reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain, in particular that contact between the viscoelastic wall and the bottom of the Fluid Cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, and of the existence of strong solutions globally in time, in the frame of interactions between a viscous Fluid and a deformable structure.

  • Existence of global strong solutions to a beam-Fluid interaction system
    Archive for Rational Mechanics and Analysis, 2016
    Co-Authors: Celine Grandmont, Matthieu Hillairet
    Abstract:

    We study an unsteady non linear Fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The Fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the Fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the Fluid Cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous Fluid and a deformable structure.

  • Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate
    SIAM Journal on Mathematical Analysis SIAM Journal of Mathematical Analysis, 2008
    Co-Authors: Celine Grandmont
    Abstract:

    We consider a three--dimensional viscous incompressible Fluid governed by the Navier--Stokes equations, interacting with an elastic plate located on one part of the Fluid boundary. We do not neglect the deformation of the Fluid domain which consequently depends on the displacement of the structure. The purpose of this work is to study the solutions of this unsteady Fluid--structure interaction problem, as the coefficient modeling the viscoelasticity (resp. the rotatory inertia) of the plate tends to zero. As a consequence, we obtain the existence of at least one weak solution for the limit problem (Navier--Stokes equation coupled with a plate in flexion) as long as the structure does not touch the bottom of the Fluid Cavity.

Ali Akrout - One of the best experts on this subject based on the ideXlab platform.

  • Vibro-acoustic analysis of laminated double glazing using the force identification method
    Journal of Theoretical and Applied Mechanics, 2014
    Co-Authors: Mounir Ben Jdidia, Ali Akrout, Dhouha Tounsi, Tahar Fakhfakh, Mohamed Haddar
    Abstract:

    This paper presents a procedure for identifying wave forms and excitation frequencies of some forces applied on a given complex Fluid-structure coupled system by using only its vibro-acoustic response. The considered concept is called the Independent Component Analysis (ICA) which is based on the Blind Source Separation (BSS). In this work, the ICA method is exploited in order to determine the excitation force applied to a thin-film laminated double glazing system enclosing a thin Fluid Cavity and limited by an elastic joint. The dynamic response of the studied Fluid-structure coupled system is determined by finite element discretization and minimization of the homogenized energy functional of the coupled problem. This response will serve as the input for the ICA algorithm in order to extract the applied excitation.

  • Vibro-acoustic behaviour of laminated double glazing enclosing a viscothermal Fluid Cavity
    Applied Acoustics, 2009
    Co-Authors: Ali Akrout, Lotfi Hammami, Mabrouk Ben Tahar, Mohamed Haddar
    Abstract:

    Abstract This paper presents a new numerical model to investigate the vibro-acoustic behaviour of two laminated glass plates enclosing a thin viscothermal Fluid Cavity. The aim of this work is to develop an original five layer (two skins plies, two adhesive films and a core ply) laminated plate finite element by mixing Kirchhoff and Mindlin plate’s theory. The formulation is based on the theory that accounts for the transverse shear in the adhesive films and in the core. The acousto-elastic model is established in dimensionless appropriate form including the effects of viscosity and thermal conductivity of Fluid and by taking into account the Fluid-structure interaction. The discretization of the energy functional by finite element method gives after minimisation a symmetrical coupled matrix system in which the acoustic matrices are frequency dependent. Therefore, an iterative procedure is derived to determine the eigenmodes of the coupled system. The modal approach is adopted to determine the vibro-acoustic system’s response. Then, the validation of the new laminate finite element model is achieved by comparing the sandwich plate results against data obtained from literature. Subsequently, predicted responses, such as the vibration transmissibility and the transmission loss of the coupled system, for a given laminated double glazing under an imposed homogeneous pressure are presented and discussed. Numerical results show the importance of both lamination and viscothermal Fluid effects on double glazing vibro-acoustic behaviour.

  • Viscothermal Fluid effects on vibro-acoustic behaviour of double elastic panels
    International Journal of Mechanical Sciences, 2008
    Co-Authors: Ali Akrout, Lotfi Hammami, Chafik Karra, Mohamed Haddar
    Abstract:

    Abstract This paper deals with the vibro-acoustic behaviour of two vibrating plates coupled to a viscothermal Fluid Cavity. The acousto-elastic model is established in dimensionless appropriate form including the effects of viscosity and thermal conductivity of Fluid and taking into account the Fluid–structure interaction. The finite element method is used for the discretization of the functional of energy, which gives after minimization a symmetrical coupled matrix system in which the acoustic matrices are frequency dependent. For this purpose, an iterative procedure is derived to determine the eigenmodes of the coupled system. The modal approach is adopted to determine the vibro-acoustic system's response which the numerical results show the importance of the viscothermal effects in the case of thin Fluid layers.

  • Simulation of Viscothermal Losses on the Acoustic Behaviour of a Thin Fluid Layer Enclosed Between Two Oscillating Plates
    Building Acoustics, 2006
    Co-Authors: Chafik Karra, Ali Akrout, Lotfi Hammami, Mohamed Haddar
    Abstract:

    This article deals with a theoretical investigation for the analysis of a double-plate system enclosing a viscothermal Fluid Cavity. Dynamic equations of the coupled system are established in appropriate dimensionless form including the effects of viscosity and thermal conductivity of the Fluid. The pressure wave equation is derived in in-plane form. This equation is solved analytically in the case of oscillating plate motions in order to determine the acoustic pressure in the Cavity. Numerical results are presented for the case of two modal shapes. They show the importance of the viscothermal effects in the case of thin Fluid layers.

G. P. Raja Sekhar - One of the best experts on this subject based on the ideXlab platform.

  • Slow motion of a porous spherical particle with a rigid core in a spherical Fluid Cavity
    Meccanica, 2017
    Co-Authors: Jai Prakash, G. P. Raja Sekhar
    Abstract:

    We present an analytical study of viscous flow past a porous spherical particle composed of a rigid core inside. We consider that this particle is located inside a spherical Fluid Cavity filled with incompressible Newtonian Fluid, under the creeping flow conditions. The governing equations inside the Fluid region and the porous region are governed by Stokes equation and Brinkman equation respectively, supplemented with the corresponding mass conservation. Hydrodynamic drag and torque exerted by the Fluid on particle are obtained which are later used to obtain the translational and rotational mobility of the particle inside the spherical Cavity. In general the presence of Cavity wall retards the particle movement as a result the mobility parameter becomes smaller than unity. The boundary effect is more pronounced when the separation distance between the particle surface and the Cavity wall is less. Various limiting cases are obtained which agree with earlier existing results.