Abstract
In Chaps. 2–4, the linear models of microstructured media have been considered, the particles of which have three degrees of freedom. In this chapter, the dynamic equations of a rectangular lattice of ellipse-shaped particles and a square lattice of round particles are generalized to the nonlinear case.
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References
Erofeev, V.I.: Wave Processes in Solids with Microstructure. World Scientific Publishing. New Jersey, London, Singapore, Hong Kong, Bangalore, Taipei (2003)
Lurie A.I.: Non-Linear Theory of Elasticity, 0. 617. Elsevier (2012)
Pavlov, I.S.: On estimation of the nonlinearity coefficients of a granular medium by the structural modeling method. Vestnik Nizhegorodskogo Universiteta (Nizhny Novgorod State University Proceedings) 6, 143–152 (2012). (in Russian)
Vanin, G.A.: Gradient theory of elasticity. Mech. Solids 1, 46–53 (1999)
Pavlov, I.S., Potapov, A.I., Maugin, G.A.: A 2D granular medium with rotating particles. Int. J. Solids Struct. 43(20), 6194–6207 (2006)
Dragunov, T.N., Pavlov, I.S., Potapov, A.I.: Anharmonic interaction of elastic and orientation waves in one-dimensional crystals. Phys. Solid State. 39, 118–124 (1997)
Potapov, A.I., Pavlov, I.S.: Nonlinear waves in 1D oriented media. Acoust. Lett. 19(6), 110–115 (1996)
Potapov, A.I., Pavlov, I.S., Lisina, S.A.: Identification of nanocrystalline media by acoustic spectroscopy methods. Acoust. Phys. 56(4), 588–596 (2010)
Dyachkov, P.N.: Carbon nanotubes. Structure, properties, applications. Publishing House Binom. Laboratory of Knowledge, Moscow (2006) 296 p. (in Russian)
Eletskii, A.V.: Mechanical properties of carbon nanostructures and related materials. Phys. Uspekhi 50(3), 225–261 (2007)
Li, Chunyu, Chou, Tsu-Wei: A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487–2499 (2003)
Goldshtein, R.V., Chentsov, A.V.: A discrete-continual model for a nanotube. Mech. Solids 4, 57–74 (2005)
Smirnov, V.V., Shepelev, D.S., Manevitch, L.I.: Localization of bending vibrations in the single-wall carbon nanotubes. Nanosyst. Phys. Chem. Math. 2(2), 102–106 (2011)
Miloserdova, I.V., Pavlov, I.S.: The mathematical model of nonlinear oscillations of a layer of nanotubes. In: Proceedings of the First Russian Conference “Problems of Mechanics and Acoustics of Media with Micro- and Nanostructure: NANOMECH-2009”, pp. 175–183. Nizhny Novgorod, Russia (2009) (in Russian)
Pavlov, I.S., Potapov, A.I.: Structural models in mechanics of nanocrystalline media. Doklady Phys. 53(7), 408–412 (2008)
Fedorov, V.I.: Theory of Elastic Waves in Crystals. Plenum Press, New York, Nauka, Moscow, 1965, 1968
Kittel, C.: Introduction to Solid State Physics, 8th edn. John Wiley and Sons, Inc. (2005)
Pavlov, P.V., Khokhlov, A.F.: Physics of Solid Body: Textbook, p. 494. Visshaya School, Moscow (2000)
Tucker, J.W., Rampton, V.W.: Microwave Ultrasonics in Solid State Physics. North-Holland Publ. Comp, Amsterdam (1972)
Acknowledgments
The research was carried out within the Russian state task for fundamental scientific research for 2019–2020 (the topic No. 0035-2019-0027, the state registration No. 01201458047).
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Erofeev, V.I., Pavlov, I.S. (2021). Nonlinear Models of Microstructured Media. In: Structural Modeling of Metamaterials. Advanced Structured Materials, vol 144. Springer, Cham. https://doi.org/10.1007/978-3-030-60330-4_5
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