The problem of acoustic wave propagation in a prestrained compressible elastic half-space that interacts with a layer of viscous compressible fluid is solved using the linearized three-dimensional equations of the theory of finite strains for the half-space and the linearized three-dimensional Navier–Stokes equations for the fluid. A problem statement and an approach based on the general solutions of the linearized equations for elastic solid and fluid are applied. A dispersion equation that describes the propagation of harmonic waves in the hydro-elastic system is obtained. The dispersion curves for the normal waves in a wide frequency range are constructed. The effect of the initial stresses of the elastic half-space and the thickness of the liquid layer on the phase velocities and attenuation coefficients of acoustic waves is analyzed. It is shown that the influence of the viscosity of the fluid and the initial stresses on the wave parameters is associated with the localization properties of waves. The developed approach and the findings make it possible to establish the limits of applicability of the models of wave processes, based on different versions of the theory of small initial strains, the classical theory of elasticity, as well as the model of the ideal fluid. The numerical results are presented in the form of graphs and analyzed.
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References
I. A. Viktorov, Surface Acoustic Waves in Solids [in Russian], Nauka, Moscow (1981).
M. M. Vol’kenshtein and V. M. Levin, “Structure of a Stoneley wave at the interface between a viscous fluid and a solid,” Akust. Zh., 34, No. 4, 608–615 (1988).
A. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses, Part 1: General Principles. Waves in Unbounded Bodies and Surface Waves [in Russian], LAP LAMBERT Academic Publishing, Saarbrucken (2016).
A. N. Guz, An Introduction to the Dynamics of Compressible Viscous Fluid [in Russian], LAP LAMBERT Academic Publishing RU, Saarbrucken (2017).
A. P. Zhuk, “Stoneley waves in a prestressed medium,” Prikl. Mekh., 16, No. 1, 113–116 (1980).
B. W. Drinkwater and P. D. Wilcox, “Ultrasonic arrays for non-destructive evaluation: A review,” NDT and E Int., 39, No. 7, 525–541 (2006).
A. Gibson and J. Popovics, “Lamb wave basis for impact-echo method analysis,” J. Eng. Mech., 131, No. 4, 438–443 (2005).
A. N. Guz, “Aerohydroelasticity problems for bodies with initial stresses,” Sov. Appl. Mech., 16, No. 3, 175–190 (1980).
A. N. Guz, Dynamics of Compressible Viscous Fluid, Cambridge Scientific Publishers, Cambridge (2009).
A. N. Guz, “On the foundations of the ultrasonic non-destructive determination of stresses in near-the-surface layers of materials. Review,” J. Phys. Sci. Appl., 1, No. 1, 1–15 (2011).
A. N. Guz, “Ultrasonic nondestructive method for stress analysis of structural members and near-surface layers of materials: Focus on Ukrainian research (review),” Int. Appl. Mech., 50, No. 3, 231–252 (2014).
A. N. Guz and A. M. Bagno, “Propagation of quasi-Lamb waves in an elastic layer interacting with a viscous liquid half-space,” Int. Appl. Mech., 55, No. 5, 459–469 (2019).
A. N. Guz and A. M. Bagno, “Influence of prestresses on quasi-Lamb modes in hydroelastic waveguides,” Int. Appl. Mech., 56, No. 1, 1–12 (2020).
A. N. Guz, A. P. Zhuk, and A. M. Bagno, “Dynamics of elastic bodies, solid particles, and fluid parcels in a compressible viscous fluid (review),” Int. Appl. Mech., 52, No. 5, 449–507 (2016).
K. Y. Jhang, “Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: a review,” Int. J. Precision Eng. Manufact., 10, No. 1, 123–135 (2009).
S. S. Kessler, S. M. Spearing, and C. Soutis, “Damage detection in composite materials using Lamb wave methods,” Smart Mater. Struct., 11, No. 2, 269–279 (2002).
M. Kobayashi, S. Tang, S. Miura, K. Iwabuchi, S. Oomori, and H. Fujiki, “Ultrasonic nondestructive material evaluation method and study on texture and cross slip effects under simple and pure shear states,” Int. J. Plasticity, 19, No. 6, 771–804 (2003).
K. R. Leonard, E. V. Malyarenko, and M. K. Hinders, “Ultrasonic Lamb wave tomography,” Inverse Problems, 18, No. 6, 1795–1808 (2002).
L. Liu and Y. Ju, “A high-efficiency nondestructive method for remote detection and quantitative evaluation of pipe wall thinning using microwaves,” NDT and E Int., 44, No. 1, 106–110 (2011).
M. Ottenio, M. Destrade, and R. W. Ogden, “Acoustic waves at the interface of a pre-stressed incompressible elastic solid and a viscous fluid,” Int. J. Non-Lin. Mech., 42, No. 2, 310–320 (2007).
C. Ramadas, K. Balasubramaniam, M. Joshi, and C. V. Krishnamurthy, “Interaction of the primary anti-symmetric Lamb mode (Ao) with symmetric delaminations: numerical and experimental studies,” Smart Mater. Struct., 18, No. 8, 1–7 (2009).
N. S. Rossini, M. Dassisti, K. Y. Benyounis, and A. G. Olabi, “Methods of measuring residual stresses in components,” Materials and Design, 35, March, 572–588 (2012).
M. Spies, “Analytical methods for modeling of ultrasonic nondestructive testing of anisotropic media,” Ultrasonics, 42, No. 1–9, 213–219 (2004).
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Translated from Prikladnaya Mekhanika, Vol. 57, No. 1, pp. 3–19, January–February 2021.
This study was sponsored by the budgetary program Support of Priority Areas of Research (KPKVK 6541230).
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Guz, O.M., Bagno, O.M. Effect of the Initial Stresses on Waves in the System Consisting of a Viscous Fluid Layer and a Compressible Elastic Half-Space. Int Appl Mech 57, 1–10 (2021). https://doi.org/10.1007/s10778-021-01054-w
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DOI: https://doi.org/10.1007/s10778-021-01054-w