Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes

Hu, Yan-Gao; Liew, K.M.; Wang, Q.; He, X. Q.; Yakobson, Boris I.

doi:10.1016/j.jmps.2008.08.010

Cited by 374 publications

(157 citation statements)

References 49 publications

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“…When flexural waves are involved, non-local continuum model may take the long-range forces of nanotube atoms into account (Zhang et al 2004(Zhang et al , 2005Wang & Hu 2005;Hu et al 2008). The non-local elastic constitutive equation includes strain gradient effects by introducing a non-local length l, i.e.…”

Section: Non-local Elastic Shell Modelmentioning

confidence: 99%

Internal resonance of vibrational modes in single-walled carbon nanotubes

Shi

Huang

2009

Proc. R. Soc. A.

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We show, by molecular dynamics simulations, that 2 : 1 internal resonance may occur between a radial breathing mode (RBM) and a circumferential flexural mode (CFM) in single-walled carbon nanotubes (SWCNTs). When the RBM vibration amplitude is greater than a critical value, automatic transformations between the RBM and CFM with approximately half RBM-frequency are observed. This discovery in the discrete SWCNT atom assembly is similar to the 2 : 1 internal resonance mechanism observed in continuum shells. A non-local continuum shell model is employed to determine the critical conditions for the occurrence of observed 2 : 1 internal resonance between the RBM and CFMs based on two non-dimensional parameters and the Mathieu stability diagram.

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Section: Non-local Elastic Shell Modelmentioning

confidence: 99%

Internal resonance of vibrational modes in single-walled carbon nanotubes

Shi

Huang

2009

Proc. R. Soc. A.

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“…Using the methodology that was proposed for chain-like mechanical systems by Rašković [26] and multiple coupled structural elements by Hedrih [27], Karličić et al [28] presented a straightforward method to obtain analytical solutions for natural frequencies and critical buckling loads of multiple nanorods, nanobeams, and nanoplates systems based on the Eringen's nonlocal elasticity theory and trigonometric method. To this time, the mechanical behaviour of different nanostructures such as the longitudinal vibration of nanorods [29], transverse vibration of nanobeams [30][31][32], nanoplates [33] and nanoshells [34] with elastic properties are given in the literature.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stability of a nonlinear multiple-nanobeam system

2018

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We use the incremental harmonic balance (IHB) method to analyse the dynamic stability problem of a nonlinear multiple-nanobeam system (MNBS) within the framework of Eringen's nonlocal elasticity theory. The nonlinear dynamic system under consideration includes MNBS embedded in a viscoelastic medium as clamped chain system, where every nanobeam in the system is subjected to time-dependent axial loads. By assuming the von Karman type of geometric nonlinearity, a system of m nonlinear partial differential equations of motion is derived based on the Euler-Bernoulli beam theory and D' Alembert's principle. All nanobeams in MNBS are considered with simply supported boundary conditions. Semi-analytical solutions for time response functions of the nonlinear MNBS are obtained by using the single-mode Galerkin discretization and IHB method, which are then validated by using the numerical integration method. Moreover, Floquet theory is employed to determine the sta- method, we obtain an incremental relationship with the frequency and amplitude of time-varying axial load, which defines stability boundaries. Numerical examples show the effects of different physical and material parameters such as the nonlocal parameter, stiffness of viscoelastic medium and number of nanobeams on Floquet multipliers, instability regions and nonlinear amplitude-frequency response curves of MNBS. The presented results can be useful as a first step in the study and design of complex micro/nanoelectromechanical systems.

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“…For this purpose, numerous investigations are conducted to propose theories and methods to study the mechanical properties of such structures. Nonlocal theory that was proposed by Eringen is one of the best and commonest approaches used by researchers' community [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] . Based on this theory the stress at a reference point is a function of the strain at all neighbor points in the body.…”

Section: Introductionmentioning

confidence: 99%

Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

Hosseini

Rahmani

2018

Smart Constr Res

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Abstract:The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction. The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.

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Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes

Cited by 374 publications

References 49 publications

Internal resonance of vibrational modes in single-walled carbon nanotubes

Internal resonance of vibrational modes in single-walled carbon nanotubes

Dynamic stability of a nonlinear multiple-nanobeam system

Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

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