The interaction of nonlinear harmonic plane elastic waves in a Murnaghan material is studied theoretically. A solution that describes the interaction of horizontally and vertically polarized harmonic transverse waves is found using the perturbation method. Pumping of energy between transverse waves of different types is described. Numerical results are obtained for five types of nanocomposites
Similar content being viewed by others
References
M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Wave Theory [in Russian], Nauka, Moscow (1990).
Z. A. Gol’dberg, “Interaction of plane longitudinal and transverse elastic waves,” Soviet Phys. Acoust., 6, No. 3, 306–310 (1961).
A. N. Guz, Elastic Waves in Prestressed Bodies [in Russian], in 2 vols., Naukova Dumka, Kyiv (1986).
A. N. Guz, J. J. Rushchitsky, and I. A. Guz, Introduction to the Mechanics of Nanocomposites [in Russian], Akademperiodika, Kyiv (2010).
L. K. Zarembo and V. A. Krasil’nikov, Introduction to Nonlinear Acoustics [in Russian], Nauka, Moscow (1966).
J. J. Rushchitsky and S. I. Tsurpal, Waves in Microstructural Materials [in Ukrainian], Inst. Mekh. S. P. Timoshenka, Kyiv (1998).
H. G. Hahn, Elastizitätstheorie. Grundlagen der linearen Theorie and Anwendungen auf eindimensionale, ebene und raumliche Probleme, B. G. Teubner, Stuttgart (1985).
E. A. Khotenko, “Numerical analysis of a nonlinear elastic Rayleigh wave,” Int. Appl. Mech., 48, No. 6, 719–726 (2012).
H. E. Leipholz, Theory of Elasticity, Nordhoof International Press, Amsterdam (1974).
F. D. Murnaghan, Finite Deformations in an Elastic Solids, Wiley, New York (1951).
W. Nowacki, Theoria Spræýystoúãi, PWN, Warsaw (1970).
J. J. Rushchitsky, “Self-switching of displacement waves in elastic nonlinearly deformed materials,” Comptes Rendus de l’ Académie des Sciences, Ser. IIb Mecanique, 330, No. 3, 175–180 (2002).
J. J. Rushchitsky, “Self-switching of waves in materials,” Int. Appl. Mech., 37, No. 11, 1492–1498 (2001).
J. J. Rushchitsky, “On the self-switching hypersonic waves in cubic nonlinear hyperelastic nanocomposites,” Int. Appl. Mech., 45, No. 1, 73–93 (2009).
J. J. Rushchitsky, “Analysis of a quadratic nonlinear hyperelastic longitudinal plane wave,” Int. Appl. Mech., 45, No. 2, 148–158 (2009).
J. J. Rushchitsky, Theory of Waves in Materials, Ventus Publishing ApS, Copenhagen (2011) (free e-book, bookboon.com).
J. J. Rushchitsky, Nonlinear Elastic Waves in Materials, Springer, Berlin-Heidelberg (2014).
J. J. Rushchitsky, “On a nonlinear description of Love waves,” Int. Appl. Mech., 49, No. 6, 629–640 (2013).
J. J. Rushchitsky and E. V. Savel’eva, “On the interaction of cubically nonlinear transverse plane waves in an elastic material,” Int. Appl. Mech., 42, No. 6, 661–668 (2006).
J. J. Rushchitsky, S. V. Sinchilo, and I. N. Khotenko, “Generation of the second, fourth, eighth, and subsequent harmonics by a quadratic nonlinear hyperelastic longitudinal plane wave,” Int. Appl. Mech., 46, No. 6, 649–659 (2010).
I. N. Sneddon and D. S. Berry, The Classical Theory of Elasticity, in: Flügge Encyclopedia of Physics, 3/VI, Springer Verlag, Berlin (1951), pp. 1–126.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 51, No. 6, pp. 72–79, November–December 2015.
Rights and permissions
About this article
Cite this article
Savel’eva, E.V. Interaction of Transverse Plane Waves in Nanocomposites. Int Appl Mech 51, 664–669 (2015). https://doi.org/10.1007/s10778-015-0723-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-015-0723-5