A problem is formulated for quasi-Lamb waves propagating in a prestrained elastic layer interacting with a half-space of compressible ideal fluid. The results are obtained using the three-dimensional equations of linearized theory of finite deformations for the elastic layer and the three-dimensional linearized Euler equations for the compressible ideal fluid. The problem statement and the approach are based on the general solutions of the linearized equations for elastic solid and fluid. The dispersion equations that describe the propagation of quasi-Lamb waves in hydroelastic systems over a wide frequency range are obtained. The effect of initial stresses and half-space of compressible ideal fluid and the thickness of the elastic layer on the phase velocities of quasi-Lamb modes is analyzed. The approach developed and the results obtained for wave processes allow establishing the limits of applicability of the models based on different versions of the theory of small initial deformations. The numerical results are presented in the form of graphs and are 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. N. Guz, General Issues, Vol. 1 of the two-volume series Elastic Waves in Prestressed Bodies [in Russian], Naukova Dumka, Kyiv (1986).
A. N. Guz, Propagation Laws, Vol. 2 of the two-volume series Elastic Waves in Prestressed Bodies [in Russian], Naukova Dumka, Kyiv (1986).
A. N. Guz, Dynamics of Compressible Viscous Fluid [in Russian], A.S.K., Kyiv (1998).
A. N. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses [in Russian], A.S.K., Kyiv (2004).
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. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses, Part 2: Waves in Partially Bounded Bodies [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. N. Guz, A. P. Zhuk, and F. G. Makhort, Waves in a Prestressed Layer [in Russian], Naukova Dumka, Kyiv (1976).
A. P. Zhuk, “Stoneley waves in a prestressed medium,” Prikl. Mekh., 16, No. 1, 113–116 (1980).
S. Yu. Babich, A. N. Guz, and A. P. Zhuk, “Elastic waves in bodies with initial stresses,” Int. Appl. Mech., 15, No. 4, 277–291 (1979).
A. M. Bagno, “Wave propagation in an elastic layer interacting with a viscous liquid layer,” Int. Appl. Mech., 52, No. 2, 133–139 (2016).
A. M. Bagno, “Effect of prestresses on the dispersion of quasi-Lamb waves in the system consisting of an ideal liquid layer and a compressible elastic layer,” Int. Appl. Mech., 53, No. 2, 139–148 (2017).
A. M. Bagno and A. N. Guz, “Elastic waves in pre-stressed bodies interacting with a fluid (survey),” Int. Appl. Mech., 33, No. 6, 435–463 (1997).
B. W. Drinkwater and P. D. Wilcox, “Ultrasonic arrays for non-destructive evaluation: A review,” NDT & 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,” Int. Appl. Mech., 16, No. 3, 175–190 (1980).
A. N. Guz, “Elastic waves in bodies with initial (residual) stresses,” Int. Appl. Mech., 38, No. 1, 23–59 (2002).
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, June, 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, 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. Precis. 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 & 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 & Design, 35, 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. 54, No. 5, pp. 3–19, September–October, 2018.
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Guz, A.N., Bagno, A.M. Effect of Prestresses on Lamb Waves in a System Consisting of an Ideal Liquid Half-Space and an Elastic Layer. Int Appl Mech 54, 495–505 (2018). https://doi.org/10.1007/s10778-018-0902-2
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DOI: https://doi.org/10.1007/s10778-018-0902-2