The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.

Intrinsic ripples in graphene

We show that the Raman scattering technique can give complete structural information for one-dimensional systems, such as carbon nanotubes. Resonant confocal micro-Raman spectroscopy of an (n,m) individual single-wall nanotube makes it possible to assign its chirality uniquely by measuring one radial breathing mode frequency omega(RBM) and using the theory of resonant transitions. A unique chirality assignment can be made for both metallic and semiconducting nanotubes of diameter d(t), using the parameters gamma(0) = 2.9 eV and omega(RBM) = 248/d(t). For example, the strong RBM intensity observed at 156 cm(-1) for 785 nm laser excitation is assigned to the (13,10) metallic chiral nanotube on a Si/SiO2 surface.

Structural (n,m) determination of isolated single wall carbon nanotubes by resonant Raman scattering

Static response and free vibration analysis of FGM plates using higher order shear deformation theory

https://northumbria-test.eprints-hosting.org/id/document/265204

A review of continuum mechanics models for size-dependent analysis of beams and plates

A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams

Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium

Vibration analysis of functionally graded thin-walled rotating blades under high temperature supersonic flow using the differential quadrature method

An analytical approach for free vibration analysis of all edges simply-supported double-orthotropic nanoplates is presented. The two nanoplates are assumed to be bonded by an internal elastic medium and surrounded by external elastic foundation. The governing equations are derived based on the nonlocal theory and the expressions of the natural frequencies are proposed in an explicit form. The suggested model is justified by a good agreement between the results given by present model and available data in literature. The model is used to study the vibration of double-orthotropic nanoplates for three typical deformation modes. The influences of small scale coefficient, stiffness of the external and internal mediums and aspect ratio on the frequencies of the double-orthotropic nanoplates are also elucidated.

Seyed Ahmad Fazelzadeh

Papers

Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium

Vibration analysis of functionally graded thin-walled rotating blades under high temperature supersonic flow using the differential quadrature method

Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium

Nonlocal inflected nano-beams: A stress-driven approach of bi-Helmholtz type

Bending-torsional flutter of wings with an attached mass subjected to a follower force