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IssuesArchive of Issues2013-5pp.509-513

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V.V. Alekhin, B.D. Annin, A.V. Babichev, and S.N. Korobeinikov, "Natural Vibrations and Buckling of Graphene Sheets," Mech. Solids. 48 (5), 509-513 (2013)
Year 2013 Volume 48 Number 5 Pages 509-513
DOI 10.3103/S0025654413050051
Title Natural Vibrations and Buckling of Graphene Sheets
Author(s) V.V. Alekhin (Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, pr-t akad. Lavrentyeva 15, Novosibirsk, 630090 Russia, alekhin@hydro.nsc.ru)
B.D. Annin (Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, pr-t akad. Lavrentyeva 15, Novosibirsk, 630090 Russia, annin@hydro.nsc.ru)
A.V. Babichev (Sobolev Institute of Geology and Mineralogy, Siberian Branch of Russian Academy of Sciences, pr-t akad. Koptyuga 3, Novosibirsk, 630090 Russia, babichev@igm.nsc.ru)
S.N. Korobeinikov (Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, pr-t akad. Lavrentyeva 15, Novosibirsk, 630090 Russia, s.n.korobeynikov@mail.ru)
Abstract Since the discovery of graphene in stable state (2004), these nanostructures have been actively used in nanotechnology. The determination of natural frequencies, mode shapes, critical compressing loads, and buckling modes of these sheets is of great theoretical and practical importance for estimating their working characteristics. To this end, in the present paper we apply the method of molecular mechanics, which was used in the authors' earlier studies to solve the problems of natural vibrations, stability, and contact for carbon nanotubes.
Keywords nanostructure, graphene, molecular mechanics, vibration, buckling
References
1.  S. N. Korobeinikov, "Nonlinear Equations of Deformation of Atomic Lattices," Arch. Mech. 57, 435-453 (2005).
2.  B. D. Annin, S. N. Korobeinikov, and A. V. Babichev, "Computer Sumulation of Nanotube Buckling in Torsion," Sib. Zh. Industrial. Mat. 11 (1), 3-22 (2008).
3.  B. D. Annin, V. V. Alekhin, A. V. Babichev, and S. N. Korobeinikov, "Computer Simulation of Nanotube Contact," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 56-76 (2010) [Mech. Solids (Engl. Transl.) 45 (3), 352-369 (2010)].
4.  B. D. Annin, V. V. Alekhin, A. V. Babichev, and S. N. Korobeinikov, "Molecular Mechanics Method Applied to Problems of Stability and Natural Vibrations of Single-Layer Carbon Nanotubes," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 65-83 (2012) [Mech. Solids (Engl. Transl.) 47 (5), 544-559 (2012)].
5.  S. N. Korobeinikov, V. V. Alyokhin, B. D. Annin, and A. V. Babichev, "Using Stability Analysis of Discrete Elastic Systems to Study the Buckling of Nanostructures," Arch. Mech. 64 (4), 367-404 (2012).
6.  S. N. Korobeinikov, Nonlinear Deformation of Solids (Sib. Otdel. RAN, Novosibirsk, 2000) [in Russian].
7.  S. L. Mayo, B. D. Olafson, and W. A. Goddard III, "A Generic Force Field for Molecular Simulation," J. Phys. Chem. 94, 8897-8909 (1990).
8.  J. Wackerfuss, "Molecular Mechanics in the Context of the Finite Element Method," Int. J. Numer. Meth. Engng 77 (7), 969-997 (2009).
9.  S. N. Korobeinikov, V. P. Agapov, M. I. Bondarenko, and A. N. Soldatkin, "The General Purpose Nonlinear Finite Element Structural Program PIONER," in Proc. Int. Conf. on Numerical Methods and Applications (Publ. House of the Bulgarian Acad. Of Sci., Sofia, 1989), pp. 228-233.
10.  S. S. Gupta and R. C. Batra, "Elastic Properties and Frequencies of Free Vibrations of Single-Layer Graphene Sheets," J. Comput. Theor. Nanosci. 7, 1-14 (2010).
11.  M. A. Lavrentiev and A. Yu. Ishlinsky, "Dynamic Buckling Modes of Elastic Systems," Dokl. Akad. Nauk SSSR 64 (6), 776-782 (1949).
Received 20 May 2013
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