Multiscale nonlinear frequency response analysis of single-layered graphene sheet under impulse and harmonic excitation using the atomistic finite element method

The atomistic finite element method (AFEM) is a multiscale technique where a sequential mode is used to transfer information between two length scales to model and simulate nanostructures at the continuum level. This method is used in this paper to investigate the nonlinear frequency response of a single-layered graphene sheet (SLGS) for impulse and harmonic excitation. The multi-body interatomic Tersoff–Brenner (TB) potential is used to represent the energy between two adjacent carbon atoms. Based on the TB potential, the equivalent geometric and elastic properties of carbon–carbon bonds are derived which are consistent with the material constitutive relations. These properties are used further to derive the nonlinear material model (stress–strain curve) of carbon–carbon bonds based on the force–deflection curve using the multi-body interatomic Tersoff–Brenner potential. A square SLGS is considered and its nonlinear vibration characteristics under an impulse and harmonic excitation for bridged, cantilever and clamped boundary conditions are investigated using the derived nonlinear material model (NMM). Before using the proposed nonlinear material model, the derived equivalent geometric and elastic properties of carbon–carbon bond are validated using molecular dynamics simulation results. The geometric (large deformation) and material nonlinearities are included in the nonlinear frequency response analysis. The investigated results of the nonlinear frequency response analysis are compared with those of the linear frequency response analysis, and the effect of the nonlinear behavior of carbon–carbon bonds on the frequency response of SLGS is studied.

[1]  W. Goddard,et al.  UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations , 1992 .

[2]  S. Adhikari,et al.  A mechanical equivalence for Poisson's ratio and thickness of C–C bonds in single wall carbon nanotubes , 2008 .

[3]  Mesut Kirca,et al.  Nonlinear failure analysis of carbon nanotubes by using molecular-mechanics based models , 2013 .

[4]  J. Tersoff,et al.  Empirical interatomic potential for carbon, with application to amorphous carbon. , 1988, Physical review letters.

[5]  S. Xiong,et al.  Band-gap modulation of graphane-like SiC nanoribbons under uniaxial elastic strain , 2014 .

[6]  Reza Ansari,et al.  Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets , 2012 .

[7]  U. Czarnetzki,et al.  Control of plasma properties in capacitively coupled oxygen discharges via the electrical asymmetry effect , 2011 .

[8]  F. Guinea,et al.  Dissipation in graphene and nanotube resonators , 2007, 0704.2225.

[9]  Paraskevas Papanikos,et al.  Finite element modeling of single-walled carbon nanotubes , 2005 .

[10]  A. J. Gil,et al.  The bending of single layer graphene sheets: the lattice versus continuum approach , 2010, Nanotechnology.

[11]  Jong-Hyun Ahn,et al.  Graphene based field effect transistors: Efforts made towards flexible electronics , 2013 .

[12]  Fabrizio Scarpa,et al.  Transverse vibration of single-layer graphene sheets , 2011 .

[13]  D. Brenner,et al.  Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. , 1990, Physical review. B, Condensed matter.

[14]  A. S. Neto,et al.  Vibrational analysis of graphene based nanostructures , 2011 .

[15]  Bruce R. Gelin,et al.  Molecular modeling of polymer structures and properties , 1994 .

[16]  Aminorroaya‐Yamini Sima,et al.  n型BiSbSTe2の結晶構造,電子構造,および熱電的性質 , 2012 .

[17]  A. Singh,et al.  Effects of van der Waals interactions on the nonlinear vibration of multi-layered graphene sheets , 2012 .

[18]  Jong-Hyun Ahn,et al.  Graphene-based transparent strain sensor , 2013 .

[19]  Pooi See Lee,et al.  Highly Stretchable Piezoresistive Graphene–Nanocellulose Nanopaper for Strain Sensors , 2014, Advanced materials.

[20]  Xiaoqun Wang,et al.  Mechanical manipulations on electronic transport of graphene nanoribbons , 2014, Journal of physics. Condensed matter : an Institute of Physics journal.

[21]  Multiscale Analysis Approach to Find the Dynamic Characteristics of Graphene Sheet , 2014 .

[22]  James Hone,et al.  Graphene nanoelectromechanical systems , 2013, Proceedings of the IEEE.

[23]  A. Singh,et al.  Atomic lattice structure and continuum plate theories for the vibrational characteristics of graphenes , 2011 .

[24]  Huajian Gao,et al.  Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model , 2003 .

[25]  M. Najjari,et al.  New modeling of the power diode using the VHDL-AMS language , 2008 .

[26]  He Tian,et al.  Single-layer graphene sound-emitting devices: experiments and modeling. , 2012, Nanoscale.

[27]  A. Zettl,et al.  Electrostatic Graphene Loudspeaker , 2013, 1303.2391.

[28]  Chunyu Li,et al.  A STRUCTURAL MECHANICS APPROACH FOR THE ANALYSIS OF CARBON NANOTUBES , 2003 .

[29]  F. Scarpa,et al.  Vibrational characteristics of bilayer graphene sheets , 2011 .