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Research Papers

Wave Propagation in Periodically Supported Nanoribbons: A Nonlocal Elasticity Approach

[+] Author and Article Information
Giuliano Allegri

Advanced Composites Centre for Innovation and Science (ACCIS),
University of Bristol,
Bristol BS8 1TR, UK
e-mail: giuliano.allegri@bristol.ac.uk

Fabrizio Scarpa

Bristol Centre for Nanoscience and Quantum Information (NSQI),
University of Bristol,
Bristol BS8 1TR, UK
e-mail: f.scarpa@bristol.ac.uk

Rajib Chowdhury

Department of Civil Engineering,
Indian Institute of Technology,
Roorkee 247 667, India
e-mail: Rajibfce@Iitr.ernet.in

Sondipon Adhikari

Multidisciplinary Nanotechnology Centre,
Swansea University,
Swansea SA2 8PP, UK
e-mail: s.adhikari@swansea.ac.uk

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 30, 2012; final manuscript received February 15, 2013; published online June 6, 2013. Assoc. Editor: Massimo Ruzzene.

J. Vib. Acoust 135(4), 041017 (Jun 06, 2013) (8 pages) Paper No: VIB-12-1127; doi: 10.1115/1.4023953 History: Received April 30, 2012; Revised February 15, 2013

We develop an analytical formulation describing propagating flexural waves in periodically simply supported nanoribbons by means of Eringen's nonlocal elasticity. The nonlocal length scale is identified via atomistic finite element (FE) models of graphene nanoribbons with Floquet's boundary conditions. The analytical model is calibrated through the atomistic finite element approach. This is done by matching the nondimensional frequencies predicted by the analytical nonlocal model and those obtained by the atomistic FE simulations. We show that a nanoribbon with periodically supported boundary conditions does exhibit artificial pass-stop band characteristics. Moreover, the nonlocal elasticity solution proposed in this paper captures the dispersive behavior of nanoribbons when an increasing number of flexural modes are considered.

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Figures

Grahic Jump Location
Fig. 1

(a) 100 GHz transistor design based on Ref. [16]. (b) Scheme of the periodically supported nanoribbon considered in this work.

Grahic Jump Location
Fig. 2

Comparison between predicted natural frequencies for (8,0) nanoribbons at different length when considering the atomistic-FE approach and molecular mechanics models (from Ref. [15])

Grahic Jump Location
Fig. 3

First six mode shapes of a (8,0) nanoribbon with 1780 atoms. (a) 4.24 GHz, (b) 16.90 GHz, (c) 38.15 GHz, (d) 67.80 GHz, (e) 105.87 GHz, and (f) 152.34 GHz.

Grahic Jump Location
Fig. 4

Dispersion curve for the (8,0) periodically supported nanoribbon with 1780 atoms. The darker lines represent flexural modes; the lighter ones are related to torsional modes.

Grahic Jump Location
Fig. 5

Actual mode shapes of the first six nondimensional frequencies Ω for the reference (8,0) nanoribbon with 1780 atoms. Case k=π. (a) Ω1, (b) Ω2, (c) Ω3, (d) Ω5, (e) Ω5, (f) Ω6.

Grahic Jump Location
Fig. 6

Effect of the nonlocality parameter e0 on the first dispersion curve

Grahic Jump Location
Fig. 7

Atomistic-FE results (dark lines) and analytical nonlocal model (light lines) for different lengths L of the periodic simply supported nanoribbon. Five modes used for the identification on the nonlocal parameter e0.

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