Vibration analysis of single-walled carbon nanotubes using different gradient elasticity theories

Ansari, R.; Gholami, R.; Rouhi, H.

doi:10.1016/j.compositesb.2012.05.049

Cited by 88 publications

(45 citation statements)

References 28 publications

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“…However, in order to consider this effect, one should consider Timoshenko or higher-order shear deformation beam theories. From the literature [18], we can see that the effect of transverse shear deformation leads to lower vibration frequencies comparing to the case with Euler-Bernoulli beam. This effect is more prominent in higher vibration modes.…”

Section: Scope and Limitations Of The Presented Modelmentioning

confidence: 83%

“…Aydogdu [17] employed the Euler-Bernoulli, Timoshenko, Levinson, Reddy, and Aydogdu beam theories to analyse the bending, buckling, and vibration of nanobeams in an analytical manner. Ansari et al [18,19] compared results obtained from nonlocal continuum mechanics with the results obtained by molecular dynamic simulations for simple models of nanostructures and concluded that the results obtained from both theories are in good agreement. More complex nanoscale systems consist of two and more organized nanostructures such as rods, beams, and plates, which are usually coupled through some medium.…”

Section: Introductionmentioning

confidence: 96%

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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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Section: Scope and Limitations Of The Presented Modelmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 96%

Dynamic stability of a nonlinear multiple-nanobeam system

2018

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“…Mechanical behaviors of such small scale structures are generally predicted by modeling them as beam, having thickness typically in the order of microns [31] or nanometers [32,33]. The size dependence of deformation behavior of micro and nano scale beams has been observed in various occasions, experimentally [34][35][36] and through molecular dynamics based simulation [37]. Conventional continuum mechanics based elasticity theories can not predict such size dependent deformation characteristics.…”

Section: Micro and Nano Scale Beam Theoriesmentioning

confidence: 99%

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Ghuku

Saha

2017

IJET

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Abstract. The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence, the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

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“…Subsequently, much progress on nonlinear problems of nanostructures with the nonlocal elasticity theory has been reported [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. The deformation and vibration of nanobeam have been studied by Lim [6][7] and Reddy [8], the assessment of nanotube structures has been investigated by Kiani K [9].…”

Section: Introductionmentioning

confidence: 99%

“…The studies on buckling of nanotubes have been reported in various references [10][11][12][13]. In addition, plenty of research results on nanotubes vibration have been reported recently [14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Resonance and Safe Basin of Single-Walled Carbon Nanotubes with Strongly Nonlinear Stiffness under Random Magnetic Field

Lim

et al. 2018

Preprint

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Abstract:In this paper, a kind of single-walled carbon nanotube nonlinear model is developed, and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of microstructure is considered based on the theory of nonlocal elasticity. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided.Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.

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Vibration analysis of single-walled carbon nanotubes using different gradient elasticity theories

Cited by 88 publications

References 28 publications

Dynamic stability of a nonlinear multiple-nanobeam system

Dynamic stability of a nonlinear multiple-nanobeam system

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Stochastic Resonance and Safe Basin of Single-Walled Carbon Nanotubes with Strongly Nonlinear Stiffness under Random Magnetic Field

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