Some boundary value problems and models for coupled elastic bodies

Arango, Jaime; Lébedev, Leonid P.; Vorovich, I.I.

doi:10.1090/qam/1604825

Cited by 2 publications

(2 citation statements)

References 4 publications

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“…Note that we omitted all physical constants for simplicity. Concerning the modelling of plate-membrane systems and more detailed models including physical constants, we refer to, e.g., [6], [15], and [19].…”

Section: Introductionmentioning

confidence: 99%

Regularity and asymptotic behavior for a damped plate–membrane transmission problem

Martínez

Denk

Monzón

et al. 2019

Journal of Mathematical Analysis and Applications

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Section: Introductionmentioning

confidence: 99%

Regularity and asymptotic behavior for a damped plate–membrane transmission problem

Martínez

Denk

Monzón

et al. 2019

Journal of Mathematical Analysis and Applications

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“…Since the multilayer system corresponds to one three-dimensional medium coupled with two two-dimensional media, the interface conditions between the layers have to be constructed. Such a method was presented in [50] for the case of a plate in bending mode coupled with a three-dimensional elastic media. In this paper, an extension to the case of the above multilayer system is presented [51].…”

Section: Introductionmentioning

confidence: 99%

Equivalent acoustic impedance model. Part 2: analytical approximation

Faverjon¹,

Soize²

2004

Journal of Sound and Vibration

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To cite this version:B. Faverjon, Christian Soize. Equivalent acoustic impedance model. Part 2: analytical approximation. Journal of Sound and Vibration, Elsevier, 2004, 276 (3-5) In the context of the prediction of noise levels in vibroacoustic systems, numerical models or analytical models can be developed. Generally, numerical models are adapted to the low and medium frequency ranges and analytical models to the medium and high frequency ranges. For analytical models, a classical approximation consists in modelling the multilayer system by an equivalent acoustic impedance. This paper deals with a multilayer system constituted of a porous medium inserted between two thin plates. Part I of this paper is devoted to the experiments performed and to the development of a probabilistic algebraic model for the equivalent acoustic impedance. In the present Part II, an analytical method is constructed for this multilayer system. This method consists in introducing the unbounded medium in the plane directions x 1 and x 2 while the medium is bounded in the x 3 direction. A two-dimensional space Fourier transform introducing the wave vector coordinates k 1 and k 2 is used. For a given frequency and for k 1 and k 2 fixed, the boundary value problem in x 3 is constituted of 12 differential equations in x 3 whose coefficients depend on k 1 and k 2 , with boundary conditions. This system of equations is solved by using adapted algebraic calculations. By inverse Fourier transform with respect to k 1 and k 2 , the equivalent acoustic impedance is deduced. The method which is proposed is not usual. Finally, a comparison of this analytical approach is compared with the experimental results.

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Some boundary value problems and models for coupled elastic bodies

Cited by 2 publications

References 4 publications

Regularity and asymptotic behavior for a damped plate–membrane transmission problem

Regularity and asymptotic behavior for a damped plate–membrane transmission problem

Equivalent acoustic impedance model. Part 2: analytical approximation

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