| Title | On the influence of a layer of a viscous compressible fluid on the surface instability of the incompressible elastic half-plane exposed to finite initial deformations |
| Publication Type | Journal Article |
| Year of Publication | 2020 |
| Authors | Bagno, AM |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2020.04.025 |
| Issue | 4 |
| Section | Mechanics |
| Pagination | 25-33 |
| Date Published | 4/2020 |
| Language | Russian |
| Abstract | The problem of propagation of harmonic waves in the pre-deformed incompressible elastic half-space that interacts with a layer of an viscous compressible fluid is considered. The study is based on the three-dimensional linearized equations of theory of elasticity of finite deformations for the incompressible elastic half-space and the three-dimensional linearized Navier—Stokes equations for a layer of a viscous compressible fluid. The approach based on the utilization of representations of general solutions of the linearized equations for an elastic solid and a fluid is applied. A dispersion equation, which describes propagation of harmonic waves in a hydroelastic system, is obtained. The dispersion curve for surface waves over a wide range of frequencies is constructed. The effects of finite initial deformations of the elastic half-space and of the thickness of the layer of a viscous compressible fluid on the phase velocities, attenuation coefficients, dispersion of the surface waves, and surface instability of a hydroelastic waveguide are 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 viscous compressible fluid, phase velocity, surface instability, surface waves |
1. Guz, A. N. (2016). Elastic waves in bodies with initial (residual) stresses. 2 parts. Saarbrucken: LAMBERT Acad. Publ. (in Russian).
2. Guz, A. N. (1998). Dynamics of compressible viscous fluid. Kiev: A.C.K. (in Russian).
3. Guz, A. N. (2009). Dynamics of compressible viscous fluid. Cambridge: Cambridge Sci. Publ.
4. Guz, A. N. (2017). Introduction to dynamics of compressible viscous fluid. Saarbrucken: LAMBERT Acad. Publ. RU (in Russian).
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., Zhuk, A.P. & Makhort, F.G. (1976). Waves in layer with initial stresses. Kiev: Naukova Dumka (in Russian).
7. Guz, A. N. (1973). Stability of elastic bodies under finite deformations. Kiev: Naukova Dumka (in Russian).
8. 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
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. Viktorov, I. A. (1981). Sound surface waves in solids. Moscow: Nauka (in Russian).
12. 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. Doi: https://doi.org/10.15407/dopovidi2018.06.040 (in Russian).
13. Bagno, A. M. (2020). On the influence of layer of an ideal compressible fluid on the surface instability of incompressible elastic half-space exposed to the finite initial deformations. Dopov. Nac. acad. nauk Ukr., No. 1, pp. 24-32. Doi: https://doi.org/10.15407/dopovidi2020.01.024
