On the acoustic waves in a layer of a viscous fluid interacting with the elastic half-space

TitleOn the acoustic waves in a layer of a viscous fluid interacting with the elastic half-space
Publication TypeJournal Article
Year of Publication2018
AuthorsGuz, AN, Bahno, AM
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2018.06.040
Issue6
SectionMechanics
Pagination40-48
Date Published6/2018
LanguageRussian
Abstract

The problem of acoustic wave propagation in a layer of a viscous compressible fluid that interacts with the elastic half-space is considered. The study is conducted on the basis of the three-dimensional linear equations of the classical elasticity theory for a solid body and on the basis of the three-dimensional linearized Navier—Stokes equations for a viscous compressible fluid. The problem formulation and the approach based on the utilization of the representations of general solutions of the linearized equations for elastic solids and liquids are applied. A dispersion equation, which describes the propagation of harmonic waves in a hydroelastic system, is obtained. The dispersion curves for normal waves over a wide range of frequencies are constructed. The influence of the thickness of the layer of a viscous compressible fluid on the phase velocities and the attenuation coefficients of acoustic waves is analyzed. It is shown that the influence of the viscosity of a fluid on the wave process parameters is associated with the localization properties of waves. The approach developed and the results obtained make it possible to establish limits for the wave processes, within which the model of an ideal compressible fluid can be applied. The numerical results are presented in the form of graphs, and their analysis is given.

Keywordsacoustic waves, attenuation coefficient, elastic half-space, layer of a viscous compressible fluid, phase velocity
References: 
  1. Viktorov, I. A. (1981). Sound surface waves in solids. Moscow: Nauka (in Russian).
  2. Bezrukov, A. V., Prikhod'ko, V. Yu. & Tyutekin, V. V. (1987). Calculation of normal wave characteristics in the case of shallow sea with an elastic bottom (the impedance method). Acoustic J., 33, No. 5, pp. 805-813 (in Russian).
  3. Bezrukov, A. V. (1989). Some propagation features of normal waves in a shallow sea with inhomogeneous elastic bottom. Acoustic J., 35, No. 4, pp. 744-747 (in Russian).
  4. Belyankova, T. I. & Kalinchuk, V. V. (2014). On the problem of analyzing the dynamic properties of a layered half-space. Acoustic J., 60, No. 5, pp. 492-504 (in Russian). doi: https://doi.org/10.1134/S1063771014050017
  5. Kuznetsov, S. V. (2014). Lamb waves in anisotropic plates (review). Acoustic J., 60, No. 1, pp. 90-100 (in Russian). doi: https://doi.org/10.1134/S1063771014010084
  6. Bagno, A. M. & Guz, A. N. (1997). Elastic waves in pre-stressed bodies interacting with a fluid (survey). Int. Appl. Mech., 33, No. 6, pp. 435-463. doi: https://doi.org/10.1007/BF02700652
  7. Guz, A. N. (2000). Compressible, viscous fluid dynamics (review). Part 1. Int. Appl. Mech., 36, No 1, pp. 14-39. doi: https://doi.org/10.1007/BF02681958
  8. Guz, A. N. (2000). The dynamics of a compressible viscous liquid (review). II. Int. Appl. Mech., 36, No. 3, pp. 281-302. doi: https://doi.org/10.1007/BF02681914
  9. Guz, A. N. (2009). Dynamics of compressible viscous fluid, Cambridge: Cambridge Scientific Publishers.
  10. Guz, A. N., Zhuk, A. P. & Bagno, A. M. (2016). Dynamics of elastic bodies, solid particles, and fluid parcels in a compressible viscous fluid (review). Int. Appl. Mech., 52, No. 5, pp. 449-507. doi: https://doi.org/10.1007/s10778-016-0770-6
  11. Guz, A. N. (1980). Aerohydroelasticity problems for bodies with initial stresses. Int. Appl. Mech., 16, No. 3, pp. 175-190. doi: https://doi.org/10.1007/BF00885084
  12. Guz, A. N. (1986). Elastic waves in bodies with initial stresses. 2 vols. Kyiv: Naukova Dumka (in Russian).
  13. Guz, A. N. (2004). Elastic waves in bodies with initial (residual) stresses. Kyiv: A.S.K. (in Russian).
  14. Guz, A. N. (1998). Dynamics of compressible viscous fluid. Kyiv: A.S.K. (in Russian).
  15. Volkenstein, M. M. & Levin, V. M. (1988). Structure of Stoneley wave on the boundary of a viscous liquid and a solid. Acoustic J., 34, No. 4, pp. 608-615 (in Russian).