| Title | On the effect of finite initial deformations on the phase velocities of normal waves in the elastic half-space interacting with the layer of an ideal compressible fluid |
| Publication Type | Journal Article |
| Year of Publication | 2019 |
| Authors | Bahno, OM |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2019.01.023 |
| Issue | 1 |
| Section | Mechanics |
| Pagination | 23-32 |
| Date Published | 01/2019 |
| Language | Russian |
| Abstract | The problem of propagation of normal waves in a pre-deformed elastic half-space that interacts with the layer of an ideal compressible fluid is considered. The study is conducted on the basis of the three-dimensional linearized equations of elasticity theory for finite deformations in the compressible and incompressible elastic half-spaces and on the basis of the three-dimensional linearized Euler equations for an ideal compressible fluid. The problem formulation and the approach based on the utilization of representations of general solutions of the linearized equations for elastic solid and fluid are applied. The dispersion equations, which describe the propagation of harmonic waves in hydroelastic systems, are obtained. The dispersion curves for normal waves over a wide range of frequencies are constructed. The effects of finite initial deformations of the elastic half-space and the thickness of the layer of an ideal compressible fluid on the phase velocities of harmonic waves are analyzed. It is shown that the influence of initial deformations of the elastic half-space on the wave process parameters is associated with the localization properties of waves. A criterion for the existence of the normal waves in hydroelastic waveguides is proposed. The approach developed and the results obtained make it possible to establish, for the wave processes, the limits of applicability of the models based on different versions of the theory of small initial deformations and the classical elasticity theory for a solid body. The numerical results are presented in the form of graphs, and their analysis is given. |
| Keywords | compressible and incompressible elastic half-spaces, dispersion of waves, initial stresses, layer of an ideal compressible fluid, normal waves |
1. Viktorov, I. A. (1981). Sound surface waves in solids. Moscow: Nauka (in Russian).
2. 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
3. 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
4. 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
5. Guz, A. N. (1986). Elastic waves in bodies with initial stresses. In 2 v. Kiev: Naukova Dumka (in Russian).
6. Guz, A. N. (2016). Elastic waves in bodies with initial (residual) stresses. 2 parts. Saarbrucken: LAP LAMBERT Academic Publishing (in Russian).
7. Guz, A. N. (1998). Dynamics of compressible viscous fluid. Kiev: A.C.K. (in Russian).
8. Guz, A. N. (2009). Dynamics of compressible viscous fluid. Cambridge: Cambridge Scientific Publishers.
9. Guz, A. N. (2017). Introduction to dynamics of compressible viscous fluid. Saarbrucken: LAP LAMBERT Academic Publishing RU (in Russian).
10. Guz, A. N. (1979). Stability of elastic bodies under hydrostatic pressure. Kiev: Naukova Dumka (in Russian).
11. Guz, A. N. (1973). Stability of elastic bodies under finite deformations. Kiev: Naukova Dumka (in Russian).
12. 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
13. Zhuk, A. P. J. (1980). Stoneley wave in a medium with initial stresses. J. Appl. Mech., 16, No. 1, pp. 113-116 (in Russian).
14. Guz, A. N., Makhort, F. G. & Guscha, O. I. (1977). Introduction in acoustoelasticity. Kiev: Naukova Dumka (in Russian).
15. Bagno, A. M. (2018). On the localization of surface waves in the layer of an ideal compressible fluid interacting with the elastic half-space. Dopov. Nac. acad. nauk Ukr., No. 1, pp. 22-28 (in Russian). doi: https://doi.org/10.15407/dopovidi2018.01.022
