Analysis of nonlinear vibration for embedded carbon nanotubes

Fu, Yiming; Hong, Jiawang; Wang, Xianqiao

doi:10.1016/j.jsv.2006.02.024

Cited by 192 publications

(116 citation statements)

References 12 publications

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“…It can be seen that as the spring constant k increases, the nonlinear frequencies tend to approach the linear ones especially when exceeds the value 10 7 n/m 2 . It should be noted that from this figure is exactly the same as the figure obtained via incremental harmonic balance method (IHBM) [2] and Adomian decomposition method ( [16], [17]). …”

Section: Case 1:nonlinear Vibration Of the Swntmentioning

confidence: 55%

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Analytical Study for the Nonlinear Vibrations of Multiwalled Carbon Nanotubes using Homotopy Analysis Method

Khader¹,

Sweilam²,

EL-Sehrawy³

et al. 2014

Appl. Math. Inf. Sci.

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Abstract:In this article, the homotopy analysis method (HAM) is implemented for obtaining semi-analytical solutions to the problem of the nonlinear vibrations of multiwalled carbon nanotubes embedded in an elastic medium. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the Van der Waals inter layer forces. The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled and triple-walled carbon nanotubes are obtained. The influence of changes in material constants of the surrounding elastic medium and the effect of changes in nanotube geometrical parameters on the vibration characteristics are studied by comparing the results with those from the previous work. Series solutions of the problem under consideration are developed by means of HAM and the recurrence relations are given explicitly. The obtained numerical results show the rapid convergence of the series constructed by the proposed method to the exact solution. Test problems have been considered to ensure that HAM is accurate and efficient compared with the Adomian decomposition method.

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Section: Case 1:nonlinear Vibration Of the Swntmentioning

confidence: 55%

“…Consider the SWNT of length l, Young's modulus E, density ρ, cross-sectional area A, and cross-sectional inertia moment I, embedded in an elastic medium with material constant k. The nonlinear vibration equation for this CNT is in the following form [2] …”

Section: Case 1:nonlinear Vibration Of the Swntmentioning

confidence: 99%

Analytical Study for the Nonlinear Vibrations of Multiwalled Carbon Nanotubes using Homotopy Analysis Method

Khader¹,

Sweilam²,

EL-Sehrawy³

et al. 2014

Appl. Math. Inf. Sci.

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show abstract

“…(15) into the system of Eq. (14) and applying the Galerkin procedure presented in [61][62][63][64][65][66][67][68], we obtain the system of linear algebraic equations in terms of unknown increments of amplitudes A i in the following form: …”

Section: Instability Regions and Periodic Solution: Ihb Methodsmentioning

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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“…Pantano and Boyce investigated the effect of the characteristic wavelike or wrinkles on the bending mode of CNTs under considering the geometric nonlinearity and explained the phenomenon that the curve modes of CNTs decrease with the increase in the diameter of CNTs. Fu et al [14] analyzed the nonlinear vibration for embedded CNTs and got the amplitude frequency response curves of the nonlinear free vibration for the SWCNTs and DWCNTs. Yan et al [15] showed that the radial vibration modes of the inner and outer tubes of simply supported DWCNTs and concluded that the system had twice dynamical mode transitions as the frequency increased.…”

Section: Introductionmentioning

confidence: 99%

Theoretical analysis on nonlinear vibration of fluid flow in single-walled carbon nanotube

et al. 2016

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In this study, the concept of nonlocal continuum theory is used to characterize the nonlinear vibration of an embedded single-walled carbon nanotube. The Pasternak-type model is employed to simulate the interaction of the SWNTs. The parameterized perturbation method is used to solve the corresponding nonlinear differential equation. The effects of the vibration amplitude, flow velocity, nonlocal parameter, and stiffness of the medium on the nonlinear frequency variation are presented. The result shows that by increasing the Winkler constant, the nonlinear frequency decreases, especially for low vibration amplitudes. In addition, it is resulted that influence of the nonlocal parameter is greater at higher flow velocities in comparison with lower flow velocities.

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Analysis of nonlinear vibration for embedded carbon nanotubes

Cited by 192 publications

References 12 publications

Analytical Study for the Nonlinear Vibrations of Multiwalled Carbon Nanotubes using Homotopy Analysis Method

Analytical Study for the Nonlinear Vibrations of Multiwalled Carbon Nanotubes using Homotopy Analysis Method

Dynamic stability of a nonlinear multiple-nanobeam system

Theoretical analysis on nonlinear vibration of fluid flow in single-walled carbon nanotube

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