|1Bahno, OM |
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
|Dopov. Nac. akad. nauk Ukr. 2019, 4:21-30|
The problem of acoustic wave propagation in the predeformed compressible elastic half-space that interacts with the layer of a viscous compressible fluid is considered. The study is based on the three-dimensional linearized equations of the theory of elasticity of finite deformations for the elastic half-space and the three-dimensional linearized Navier—Stokes equations for a viscous compressible fluid. The problem formulation and the approach based on the representations of general solutions of the linearized equations for elastic solid and fluid are applied. A dispersion equation, which describes the propagation of harmonic waves in a hydroelastic system, is obtained. The dispersion curves for normal waves for a wide range of frequencies are constructed. The effect of initial stresses of the elastic half-space and the thickness of the layer of a viscous compressible fluid on the phase velocities and attenuation coefficients of acoustic waves are 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. An approach developed and the results obtained for the wave processes make it possible to establish the limits of applicability of the models based on different versions of the theory of small initial deformations and of the classical elasticity theory for a solid body, as well the model of an ideal fluid. The numerical results are presented in the form of graphs, and their analysis is given.
|Keywords: acoustic waves, attenuation coefficient, compressible elastic half-space, initial stresses, layer of a viscous compressible fluid, phase velocity|
1. 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
2. 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
3. Guz, A. N. (2002). Elastic waves in bodies with initial (residual) stresses. Int. Appl. Mech., 38, No. 1, pp. 23-59. doi: https://doi.org/10.1023/A:1015379824503
4. Guz, A. N. (2009). Dynamics of compressible viscous fluid. Cambridge: Cambridge Scientific Publ.
5. 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
6. Guz, A. N. (1986). Elastic waves in bodies with initial stresses. 2 vols. Kiev: Naukova Dumka (in Russian).
7. Guz, A. N. (2016). Elastic waves in bodies with initial (residual) stresses. 2 parts. Saarbrücken: LAMBERT Acad. Publ. (in Russian).
8. Guz, A. N. (1998). Dynamics of compressible viscous fluid. Kiev: A.C.K. (in Russian).
9. Guz, A. N. (2017). Introduction to dynamics of compressible viscous fluid. Saarbrücken: LAMBERT Acad. Publ. RU (in Russian).
10. Guz, A. N., Makhort, F. G. & Guscha, O. I. (1977). Introduction in acoustoelasticity. Kiev: Naukova Dumka (in Russian).
11. 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
12. 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
13. Zhuk, A. P. (1980). Stoneley wave in a medium with initial stresses. J. Appl. Mech., 16, No. 1, pp. 113-116 (in Russian).
14. Viktorov, I. A. (1981). Sound surface waves in solids. Moscow: Nauka (in Russian).
15. Guz, A. N. & Bagno, A. M. (2018). On the acoustic waves in a layer of viscous fluid interacting with the elastic half-space. Dopov. Nac. acad. nauk Ukr., No. 6, pp. 40-48 (in Russian). doi: https://doi.org/10.15407/dopovidi2018.06.040