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Journal of the Acoustical Society of America / Volume 117 / Issue 2 / GENERAL LINEAR ACOUSTICS [20]

Approximate high-order dynamic theory of a fluid layer in between two thick solids

J. Acoust. Soc. Am. Volume 117, Issue 2, pp. 518-527 (2005); (10 pages)

Dmitry D. Zakharov

FESBE, London South Bank University, 103 Borough Road, London SE1 0AA, United Kingdom

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A thin layer of heavy fluid with bound faces is considered first. For the sake of simplicity, the effects of vortex and viscosity are neglected. Two cases of compressible and incompressible fluids are treated, assuming that a thickness-over-wavelength ratio is a small parameter. For the internal state of medium the relations between the quantities on the layer surfaces are deduced. In contrast to the standard approach, which expands the propagator matrix into power series of a small wave number, the asymptotic integration of 3D equations and boundary conditions of fluid dynamics is performed. Respective relations are represented in a recurrent form and permit one to obtain the high-order components of the displacements and pressure rather simply. When considering two thick solids with a fluid in between, this result is used to derive the so-called “impedance boundary conditions” (IBC) with a relative asymptotic error up to tenth order. Tests show their validity until the first quasiresonance frequency of a layer, so, the analysis is not just long wave but essentially low frequency. Thus, these IBC are applicable to reduce the dimension in the analysis of challenged multicomponent system of fluid-coupled solids in a reasonable frequency range. © 2005 Acoustical Society of America.

© 2005 Acoustical Society of America

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KEYWORDS and PACS

Keywords

fluids, compressible flow, compressibility, computational fluid dynamics, acoustic wave propagation, ultrasonics

PACS

  • 43.20.El

    Reflection, refraction, diffraction of acoustic waves

  • 43.20.Px

    Transient radiation and scattering

  • 43.20.Tb

    Interaction of vibrating structures with surrounding medium

  • 43.35.Bf

    Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions

ARTICLE DATA

History
Received 06 Jul 2004
Accepted 01 Dec 2004
Revised 29 Nov 2004
Digital Object Identifier
http://dx.doi.org/10.1121/1.1850406

PUBLICATION DATA

ISSN

0001-4966 (print)  

Publisher

$abstract.society.value is a Member of CrossRef Acoustical Society of America

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