TY - JOUR

T1 - Continual model of deformation of graphene

AU - Morozov, N.F.

AU - Tovstik, P.E.

AU - Tovstik, T.P.

PY - 2014

Y1 - 2014

N2 - A single-layer graphene sheet is studied. It is assumed that the total potential energy of the system under consideration consists of four parts. First, the energy of stretching of the bond between two neighboring atoms (the Morse potential). Second, the energy of variations in the angle between three neighboring atoms (the Brenner potential). Third, the energy needed to remove an atom from the plane defined by three neighboring atoms. Fourth, the energy of the torsion of four neighboring atoms. The van der Waals forces are neglected. Only small strains are considered. In the long-wavelength approximation, the two-dimensional extension and flexion energy is derived. As a result, an equivalent plate with corresponding extension and flexion moduli is obtained. The free vibration frequencies of a rectangular plate are found. The stability under the compression in the plane of the plate is studied. To that end, the tangential stresses are complemented with nonlinear terms depending on the transverse displacements

AB - A single-layer graphene sheet is studied. It is assumed that the total potential energy of the system under consideration consists of four parts. First, the energy of stretching of the bond between two neighboring atoms (the Morse potential). Second, the energy of variations in the angle between three neighboring atoms (the Brenner potential). Third, the energy needed to remove an atom from the plane defined by three neighboring atoms. Fourth, the energy of the torsion of four neighboring atoms. The van der Waals forces are neglected. Only small strains are considered. In the long-wavelength approximation, the two-dimensional extension and flexion energy is derived. As a result, an equivalent plate with corresponding extension and flexion moduli is obtained. The free vibration frequencies of a rectangular plate are found. The stability under the compression in the plane of the plate is studied. To that end, the tangential stresses are complemented with nonlinear terms depending on the transverse displacements

U2 - 10.3103/S1063454114010063

DO - 10.3103/S1063454114010063

M3 - Article

SP - 47

EP - 55

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -