Propagation of elastic waves in nanostructures

This paper presents the study of propagation of elastic waves in nanostructures using continuum approximation. The wave propagation characteristics in both 1-D and 2-D nanostructures, namely the carbon nanotubes and Graphene are studied in this paper. In particular, the use of various gradient elasticity theories, namely the Eringen’s Stress gradient theory, the second and fourth order strain gradient theories, that brings in atomistic length scale parameters into the continuum governing equations, is used in this paper to study the wave propagation characteristics in the nanostructures. Using these non-local theories, wave propagation in Single and Multi-wall carbon tubes and monolayer Graphene structures are studied. A number of examples are presented that brings out the essential wave propagation features such as escape frequency, cut-off frequencies, phase speeds and group speeds in these structures.

[1]  E. Aifantis,et al.  On the structure of the mode III crack-tip in gradient elasticity , 1992 .

[2]  Y. Povstenko.  The nonlocal theory of elasticity and its applications to the description of defects in solid bodies , 1999 .

[3]  Andrei V. Metrikine,et al.  Higher-order continua derived from discrete media: continualisation aspects and boundary conditions , 2005 .

[4]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[5]  E. Aifantis.  On the role of gradients in the localization of deformation and fracture , 1992 .

[6]  E. Aifantis,et al.  On Some Aspects in the Special Theory of Gradient Elasticity , 1997 .

[7]  Joo-Hiuk Son,et al.  Terahertz conductivity of anisotropic single walled carbon nanotube films , 2002 .

[8]  James E. Butler,et al.  Elastic, mechanical, and thermal properties of nanocrystalline diamond films , 2003 .

[9]  A. Cemal Eringen,et al.  Linear theory of nonlocal elasticity and dispersion of plane waves , 1972 .

[10]  G. A. Antonelli,et al.  Picosecond ultrasonics study of the vibrational modes of a nanostructure , 2002 .

[11]  Carlo Sirtori,et al.  Applied physics: Bridge for the terahertz gap , 2002, Nature.

[12]  R. Ramprasad,et al.  Scalability of phononic crystal heterostructures , 2005 .

[13]  S. Narendar,et al.  Wave Propagation in Nanostructures , 2013 .

[14]  Boris I. Yakobson,et al.  C2F, BN, AND C NANOSHELL ELASTICITY FROM AB INITIO COMPUTATIONS , 2001 .

[15]  Andre K. Geim,et al.  Electric Field Effect in Atomically Thin Carbon Films , 2004, Science.

[16]  Ashwin Sampathkumar,et al.  Photothermal operation of high frequency nanoelectromechanical systems , 2006 .

[17]  R. D. Mindlin.  Micro-structure in linear elasticity , 1964 .

[18]  A. Eringen.  On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .

[19]  S. Guo,et al.  On Using Strain Gradient Theories In The Analysis Of Cracks , 2005 .

[20]  Bernd Schultrich,et al.  Testing ultra-thin films by laser-acoustics , 2000 .

[21]  John Peddieson,et al.  Application of nonlocal continuum models to nanotechnology , 2003 .

[22]  D. Chung,et al.  Vibration damping using flexible graphite , 2000 .

[23]  R. D. Mindlin.  MICROSTRUCTURE IN LINEAR ELASTICITY , 1999 .

[24]  H. F. Tiersten,et al.  Effects of couple-stresses in linear elasticity , 1962 .

[25]  H. V. D. Zant,et al.  Nanomechanical properties of few-layer graphene membranes , 2008, 0802.0413.

[26]  Ching S. Chang,et al.  Second-gradient constitutive theory for granular material with random packing structure , 1995 .

[27]  S. Krishnaswamy,et al.  Photoacoustic characterization of the mechanical properties of thin films , 2002 .