Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory

Ke, Liao-Liang; Xiang, Yang; Yang, Jie; Kitipornchai, S.

doi:10.1016/j.commatsci.2009.09.002

Cited by 228 publications

(91 citation statements)

References 43 publications

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“…He's variational method exhibited more advantages [12,[34][35][36][37]. The direct iterative method was used in dynamical analysis of DWCNT [38]. The finite element method [21,23] and the differential quadrature method [13,22] also exhibited more advantages.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

et al. 2018

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Abstract:In the present study, the nonlinear vibration of a nanobeam resting on the fractional order viscoelastic Winkler-Pasternak foundation is studied using nonlocal elasticity theory. The D'Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. A detailed parametric study is conducted, and the effects of the variation of different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have a significant effect on the natural frequency and the amplitude of vibrations.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

et al. 2018

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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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“…Firstly, for many micro/nano beams, both the physical (e.g., induced by van der Waals force) and geometrical (e.g., stem from large deflection) nonlinearities were observed by previous theoretical and experimental investigations (Yang et al, 2010;Ke et al, 2009), the nonlinearity causes the mechanical behaviors of the beams to be changed significantly (Setoodeh et al, 2011;Fang et al, 2013), so the linear beam theory is not appropriate in such situations. Moreover, some researches confirm that the thermal effects are effective on the mechanical behaviors of micro/nano beams (Amara et al, 2010;Ansari et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Large amplitude free vibration of micro/nano beams based on nonlocal thermal elasticity theory

Wang

Song

Lin

et al. 2015

Lat. Am. j. solids struct.

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This paper is concerned with the nonlinear free vibration of a heated micro/nano beam modeled after the nonlocal continuum elasticity theory and Euler-Bernoulli beam theory. The governing partial differential equations are derived from the Hamilton variational principle and von Kármán geometric nonlinearity, in which the effects of the nonlocality and ambient temperature are inclusive. These equations are converted into ordinary forms by employing the Kantorovich method. The solutions of nonlinear free vibration are then sought through the use of shooting method in spatial domain. Numerical results show that the proposed treatment provides excellent accuracy and convergence characteristics. The influences of the aspect ratio, nonlocal parameter and temperature rise parameter on the dimensionless radian frequency are carefully investigated. It is concluded that the nonlocal and temperature rise parameters lead to reductions of the nonlinear vibration frequency, while the influence of the nonlocal effect decreases with an increase in the aspect ratio.

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Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory

Cited by 228 publications

References 43 publications

Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

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

Large amplitude free vibration of micro/nano beams based on nonlocal thermal elasticity theory

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