Approximate Theory of Sound Propagation in a Bounded Viscoelastic Medium with Cylindrical Channels

The acoustic characteristics of a cylindrical viscoelastic tube of finite length with a radially fixed outer surface replacing the hexagonal unit cell of a segment of a micro-inhomogeneous medium with cylindrical channels are calculated. The least-action principle and the hypothesis of plane section...

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Bibliographic Details
Published in:Fluid dynamics 2022-12, Vol.57 (7), p.932-943
Main Author: Kazakov, L. I.
Format: Article
Language:English
Subjects:
Acoustic propagation
Approximation
Channels
Classical and Continuum Physics
Classical Mechanics
Engineering Fluid Dynamics
Fluid- and Aerodynamics
Inhomogeneous media
Physics
Physics and Astronomy
Principle of least action
Shear modulus
Sound propagation
Sound waves
Unit cell
Viscoelasticity
Wave propagation
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Summary:The acoustic characteristics of a cylindrical viscoelastic tube of finite length with a radially fixed outer surface replacing the hexagonal unit cell of a segment of a micro-inhomogeneous medium with cylindrical channels are calculated. The least-action principle and the hypothesis of plane sections are applied. A dispersion relation for longitudinal sound waves in a tube is found, which coincides with the approximations of the exact dispersion relation and has a form typical of micro-inhomogeneous resonant media. From a suitable approximation of the results of known measurements of the reduced input conductance of “semi-infinite” samples, the frequency dependence of the complex shear modulus of the rubber used is found.
ISSN:0015-4628
1573-8507
DOI:10.1134/S0015462822070060