Non-local approach in mathematical problems of fluid-structure interaction

Jentsch, Lothar; Natroshvili, David

doi:10.1002/(sici)1099-1476(19990110)22:1<13::aid-mma18>3.0.co;2-k

Cited by 13 publications

(16 citation statements)

References 35 publications

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“…A major drawback of the classical boundary integral formulations for the exterior Neumann problem related to the Helmholtz equation is related to the uniqueness problem, although the boundary value problem has a unique solution for all real frequencies [97,98]. Precisely, there is not a unique solution of the physical problem for a sequence of real frequencies called spurious or irregular frequencies, also called Jones eigenfrequencies [31,[128][129][130][131], and various methods are proposed in the literature to overcome this mathematical difficulty arising in the boundary element method [128,[132][133][134][135][136]. In this appendix, we present a boundary element method that was initially developed in [137] and detailed in [41].…”

Section: Appendix B Boundary Element Methods For the External Acoustimentioning

confidence: 99%

Computational Vibroacoustics in Low- and Medium- Frequency Bands: Damping, ROM, and UQ Modeling

Ohayon

Soize

2017

Applied Sciences

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Abstract:Within the framework of the state-of-the-art, this paper presents a summary of some common research works carried out by the authors concerning computational methods for the prediction of the responses in the frequency domain of general linear dissipative vibroacoustics (structural-acoustic) systems for liquid and gas in the low-frequency (LF) and medium-frequency (MF) domains, including uncertainty quantification (UQ) that plays an important role in the MF domain. The system under consideration consists of a deformable dissipative structure, coupled with an internal dissipative acoustic fluid including a wall acoustic impedance, and surrounded by an infinite acoustic fluid. The system is submitted to given internal and external acoustic sources and to prescribed mechanical forces. An efficient reduced-order computational model (ROM) is constructed using a finite element discretization (FEM) for the structure and the internal acoustic fluid. The external acoustic fluid is treated using a symmetric boundary element method (BEM) in the frequency domain. All the required modeling aspects required for the analysis in the MF domain have been introduced, in particular the frequency-dependent damping phenomena and model uncertainties. An industrial application to a complex computational vibroacoustic model of an automobile is presented.

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Section: Appendix B Boundary Element Methods For the External Acoustimentioning

confidence: 99%

Computational Vibroacoustics in Low- and Medium- Frequency Bands: Damping, ROM, and UQ Modeling

Ohayon

Soize

2017

Applied Sciences

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“…This is related to the uniqueness problem although the boundary value problem has a unique solution for all real frequencies [18,127]. Precisely, there is no unique solution of the physical problem for a sequence of real frequencies called as spurious or irregular frequencies and they are also called as Jones eigenfrequencies [112,[128][129][130][131]. Various methods are proposed in the literature to overcome this mathematical difficulty that arises in the boundary element method [3,129,[132][133][134][135][136][137].…”

Section: Symmetric Boundary Element Methods Without Spurious Frequencimentioning

confidence: 99%

Advanced Computational Dissipative Structural Acoustics and Fluid-Structure Interaction in Low-and Medium-Frequency Domains. Reduced-Order Models and Uncertainty Quantification

Ohayon¹,

Soize²

2012

International Journal of Aeronautical and Space Sciences

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This paper presents an advanced computational method for the prediction of the responses in the frequency domain of general linear dissipative structural-acoustic and fluid-structure systems, in the low-and medium-frequency do mains and this includes uncertainty quantification. The system under consideration is constituted of a deformable dissipative structure that is coupled with an internal dissipative acoustic fluid. This includes wall acoustic impedances and it is surrounded by an infinite acoustic fluid. The system is submitted to given internal and external acoustic sources and to the prescribed mechanical forces. An efficient reduced-order computational model is constructed by using a finite element discretization for the structure and an internal acoustic fluid. The external acoustic fluid is treated by using an appropriate boundary element method in the frequency domain. All the required modeling aspects for the analysis of the medium-frequency domain have been introduced namely, a viscoelastic behavior for the structure, an appropriate dissipative model for the internal acoustic fluid that includes wall acoustic impedance and a model of uncertainty in particular for the modeling errors. This advanced computational formulation, corresponding to new extensions and complements with respect to the state-of-the-art are well adapted for the development of a new generation of software, in particular for parallel computers. Key words:Computational mechanics, Structural acoustics, Vibroacoustic, Fluid-structure interaction, Uncertainty quantification, Reduced-order model, Medium frequency, Low frequency, Dissipative system, Viscoelasticity, Wall acoustic impedance, Finite element discretization, Boundary element method Nomenclature a ijkh = elastic coefficients of the structure b ijkh = damping coefficients of the structure c 0 = speed of sound in the internal acoustic fluid c E = speed of sound in the external acoustic fluid f = vector of the generalized forces for the internal acoustic fluid f S = vector of the generalized forces for the structure g = mechanical body force field in the structure i = imaginary complex number i k = wave number in the external acoustic fluid n = number of internal acoustic DOF n s = number of structure DOF n j = component of vector n n = outward unit normal to Abstract This paper presents an advanced computational method for the prediction of the responses in the frequency domain of general linear dissipative structural-acoustic and uid-structure systems, in the low-and medium-frequency domains and this includes uncertainty quantication. The system under consideration is constituted of a deformable dissipative structure that is coupled with an internal dissipative acoustic uid. This includes wall acoustic impedances and it is surrounded by an innite acoustic uid. The system is submitted to given internal and external acoustic sources and to the prescribed mechanical forces. An efcient reduced-order computational model is constructed by using a nite element discret...

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“…By Z (Ω 1 ), we denote a subclass of complex‐valued functions from

H_{l o c}^{1} false(Ω_{1} false)

satisfying the Sommerfeld radiation conditions at infinity (see Vekua and Colton and Kress for the Helmholtz operator and Vainberg and Jentsch et al for the “anisotropic” operator A 1 defined by ). Denote by S ω the characteristic surface (ellipsoid) associated with the operator A 1 ,

a_{k j}^{(1)} ξ_{k} ξ_{j} - ω^{2} κ_{1} = 0, ξ \in {double-struckR}^{3} .

For an arbitrary vector

η \in R^{3}

with | η | = 1, there exists only one point ξ ( η ) ∈ S ω such that the outward unit normal vector n ( ξ ( η )) to S ω at the point ξ ( η ) has the same direction as η , ie, n ( ξ ( η )) = η .…”

Section: Formulation Of the Transmission Problemmentioning

confidence: 99%

“…Conditions are equivalent to the classical Sommerfeld radiation conditions for the Helmholtz equation if A 1 ( ∂ ) = Δ( ∂ ) + ω 2 , ie, if κ 1 = 1 and

a_{k j}^{false(1 false)} = δ_{k j}

, where δ k j is the Kronecker delta. There holds the following analogue of the classical Rellich‐Vekua lemma (for details, see Jentsch et al and Natroshvili et al).…”

Section: Formulation Of the Transmission Problemmentioning

confidence: 99%

Singular localised boundary‐domain integral equations of acoustic scattering by inhomogeneous anisotropic obstacle

Chkadua

Mikhailov

Natroshvili

2018

Math Methods in App Sciences

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We consider the time‐harmonic acoustic wave scattering by a bounded anisotropic inhomogeneity embedded in an unbounded anisotropic homogeneous medium. The material parameters may have discontinuities across the interface between the inhomogeneous interior and homogeneous exterior regions. The corresponding mathematical problem is formulated as a transmission problems for a second‐order elliptic partial differential equation of Helmholtz type with discontinuous variable coefficients. Using a localised quasi‐parametrix based on the harmonic fundamental solution, the transmission problem for arbitrary values of the frequency parameter is reduced equivalently to a system of singular localised boundary‐domain integral equations. Fredholm properties of the corresponding localised boundary‐domain integral operator are studied and its invertibility is established in appropriate Sobolev‐Slobodetskii (Bessel potential) spaces, which implies existence and uniqueness results for the localised boundary‐domain integral equations system and the corresponding acoustic scattering transmission problem.

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Non-local approach in mathematical problems of fluid-structure interaction

Cited by 13 publications

References 35 publications

Computational Vibroacoustics in Low- and Medium- Frequency Bands: Damping, ROM, and UQ Modeling

Computational Vibroacoustics in Low- and Medium- Frequency Bands: Damping, ROM, and UQ Modeling

Advanced Computational Dissipative Structural Acoustics and Fluid-Structure Interaction in Low-and Medium-Frequency Domains. Reduced-Order Models and Uncertainty Quantification

Singular localised boundary‐domain integral equations of acoustic scattering by inhomogeneous anisotropic obstacle

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