The influence of surface effect on vibration behaviors of carbon nanotubes under initial stress

Chen, X.; Fang, Chao; Wang, X.

doi:10.1016/j.physe.2016.08.011

Cited by 15 publications

(7 citation statements)

References 31 publications

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“…Moreover, the geometric parameters of the CNTs are taken to be the outermost diameter dout=3nm, the thickness h=0.34nm, and the length l=45nm. 24–26…”

Section: Resultsmentioning

confidence: 99%

“…According to Newton’s law, the shear force can be written as follows Considering the effects the equivalent transverse load induced by thermal and longitudinal magnetic field and residual stress, the longitudinal force can be obtained as follows where Substituting equations (8) to (11) into equation (7) yields where e0a is the small-scale effect on the mechanical characteristics of nanostructures, C is the damping coefficient of viscoelastic foundation and EI* is the effective bending stiffness considering the surface effect that can be written as 24 In equation (2) Es,dout, and din are the surface modulus of the nanotube, outer diameter, and inner diameter of SWCNT, respectively. In addition, terms Hτ,P(x,t),F(t),FT(x,t), and FB(x,t) are the coefficient transverse loading corresponding to the residual surface stress, the applied load to the outermost layer, the harmonic external excitation, the equivalent transverse load induced by thermal and longitudinal magnetic field, respe...…”

Section: Appendixmentioning

confidence: 99%

“…Substituting equations (8) to (11) into equation (7) yields where e0a is the small-scale effect on the mechanical characteristics of nanostructures, C is the damping coefficient of viscoelastic foundation and EI* is the effective bending stiffness considering the surface effect that can be written as 24 …”

Section: Appendixmentioning

confidence: 99%

See 2 more Smart Citations

Chaotic vibrations of a harmonically excited carbon nanotube with consideration of thermomagnetic filed and surface effects

Azarboni

Edalatpanah

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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In the studies of the dynamic response of carbon nanotubes, the stability, predictable, and unpredictable chaotic vibrations are fundamental characteristics. In this paper, we investigate the chaotic and periodic vibrations of a single-walled carbon nanotube resting on the viscoelastic foundation, based on the nonlocal Euler–Bernoulli beam model. It is assumed that the single-walled carbon nanotube is subjected to an external harmonic excitation. The axial thermomagnetic field and the surface effect on the governing equation of single-walled carbon nanotube are taken into account. We also solve the nonlinear governing equation by using the Galerkin decomposition method along with the fourth-order Rung–Kutta numerical integration scheme. Furthermore, we analyze the effects of amplitude and frequency of excitation on the formation of chaotic and periodic regions using bifurcation diagrams and largest Lyapunov exponents. Moreover, we present the phase portrait, Poincare maps, and time history to observe the periodic and chaotic responses of the system. The results show that the nonlinear dynamic response of single-walled carbon nanotube is much more sensitive to both amplitude and frequency of excitation.

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“…Moreover, the geometric parameters of the CNTs are taken to be the outermost diameter dout=3nm, the thickness h=0.34nm, and the length l=45nm. 24–26…”

Section: Resultsmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

See 1 more Smart Citation

Chaotic vibrations of a harmonically excited carbon nanotube with consideration of thermomagnetic filed and surface effects

Azarboni

Edalatpanah

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…This section is concerned to assess and predict the post-critical buckling loads (PCL) of a truncated conical carbon nanotube (CCNT). First, in order to analyze the CCNT, the following material properties are utilized as [63][64][65][66][67][68][69][70][71][72] It is important to note that the above-mentioned quantities are averaged values and are related to an armchair carbon nanotube in a continuum schema [73][74][75][76][77][78]. As the armchair is a symmetrical nanotube, it is presumed as an isotropic beam.…”

Section: Post-buckling Of Truncated Conical Swcntsmentioning

confidence: 99%

Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Malikan

Eremeyev

2020

Mater. Res. Express

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This research predicts theoretically post-critical axial buckling behavior of truncated conical carbon nanotubes (CCNTs) with several boundary conditions by assuming a nonlinear Winkler matrix. The post-buckling of CCNTs has been studied based on the Euler-Bernoulli beam model, Hamilton's principle, Lagrangian strains, and nonlocal strain gradient theory. Both stiffness-hardening and stiffness-softening properties of the nanostructure are considered by exerting the second stressgradient and second strain-gradient in the stress and strain fields. Besides small-scale influences, the surface effect is also taken into consideration. The effect of the Winkler foundation is nonlinearly taken into account based on the Taylor expansion. A new admissible function is used in the Rayleigh-Ritz solution technique applicable for buckling and post-buckling of nanotubes and nanobeams. Numerical results and related discussions are compared and reported with those obtained by the literature. The significant results proved that the surface effect and the nonlinear term of the substrate affect the CCNT considerably.

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“…Several investigations have been carried out in recent years using the Gurtin-Murdoch elasticity theory to analyze mechanical behaviors of micro-/nanostructures. Chen et al [69] presented an analytical method to study the influence of surface stress on the free vibration analysis of carbon nanotubes under initial stress. Yue et al [70] derived a size-dependent Kirchhoff plate model including surface tension and surface tensioninduced residual stress within the framework of the Gurtin-Murdoch theory of elasticity.…”

Section: Introductionmentioning

confidence: 99%

Surface stress effect on the nonlinear free vibrations of functionally graded composite nanoshells in the presence of modal interaction

Xie

Sahmani

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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As one of the innovative materials, functionally graded (FG) composite materials have the capability to vary microstructure and design attributes from one side to other representing the desired material properties. The prime aim of this work is to analyze the surface stress effect on the nonlinear free vibration response of FG cylindrical nanoshells incorporating various modal interactions. To this end, the Gurtin-Murdoch theory of elasticity together with the von Karman geometrical nonlinearity is implemented to the classical shell theory to construct an efficient size-dependent shell model. In order to take the modal interactions between the main oscillation mode and various symmetric vibration modes, the lateral deflection of the FG nanoshell is expressed as combination of the simple main vibration mode and convergent symmetric modes. Thereafter, the solution of problem is considered as the summation of the homogenous and particular parts to put the Galerkin technique to use. Finally, the multiple timescales method is employed to achieve analytical expression for the surface elastic-based frequency response of FG nanoshells. It is displayed that in the presence of modal interaction, by increasing the shell deflection, the value of the frequency ratio decreases while in the absence of modal interaction, it enhances.

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The influence of surface effect on vibration behaviors of carbon nanotubes under initial stress

Cited by 15 publications

References 31 publications

Chaotic vibrations of a harmonically excited carbon nanotube with consideration of thermomagnetic filed and surface effects

Chaotic vibrations of a harmonically excited carbon nanotube with consideration of thermomagnetic filed and surface effects

Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Surface stress effect on the nonlinear free vibrations of functionally graded composite nanoshells in the presence of modal interaction

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