|Dopov. Nac. akad. nauk Ukr. 2020, 2:15-23|
The problem of the propagation of acoustic waves in a previously deformed incompressible elastic half-space interacting with a layer of a viscous compressible fluid is considered. The study was carried out on the basis of three-dimensional linearized equations of the theory of elasticity of finite deformations for an incompressible elastic half-space and three-dimensional linearized Navier—Stokes equations for a layer of a viscous compressible fluid. The formulation of the problem and the approach based on the use of representations of general solutions of the linearized equations for an elastic body and fluid are used. A dispersion equation describing the propagation of harmonic waves in a hydroelastic system is obtained. Dispersion curves of surface waves are constructed in a wide frequency range. The effect of the finite initial deformations of the elastic half-space and the thickness of a layer of a viscous compressible fluid on the phase velocities, attenuation coefficients, and dispersion of surface waves in hydroelastic waveguides is analyzed. The numerical results are presented in the form of graphs, and their analysis is given.
|Keywords: attenuation coefficient, finite initial deformations, incompressible elastic half-space, layer of a viscous compressible fluid, phase velocity, surface waves|
1. Viktorov, I. A. (1981). Sound surface waves in solids. Moscow: Nauka (in Russian).
2. 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
3. Guz, A. N. (2016). Elastic waves in bodies with initial (residual) stresses. 2 parts. Saarbrücken: LAMBERT (in Russian).
4. Guz, A.N. (1998). Dynamics of compressible viscous fluid. Kyiv: A.C.K. (in Russian).
5. Guz, A.N. (2009). Dynamics of compressible viscous fluid. Cambridge: Cambridge Scientific Publishers.
6. Guz, A. N. (2017). Introduction to dynamics of compressible viscous fluid. Saarbrücken: LAMBERT (in Russian).
7. 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
8. Guz, A. N., Zhuk, A. P. & Makhort, F. G. (1976). Waves in layer with initial stresses. Kyiv: Naukova Dumka (in Russian).
9. Babich, S. Y., Guz, A. N. & Zhuk, A. P. (1979). Elastic waves in bodies with initial stresses. Int. Appl. Mech., 15, No 4, pp. 277-291. Doi: https://doi.org/10.1007/BF00884760
10. Zhuk, A. P. (1980). Stoneley wave in a medium with initial stresses. J. Appl. Mech., 16, No 1, pp. 113-116 (in Russian).
11. Guz, A. N. & Bagno, A. M. (2018). On the acoustic waves in a layer of a 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