Non-conservative instability of cantilever carbon nanotubes resting on viscoelastic foundation

Kazemi-Lari, Mohammad A.; Fazelzadeh, S. Ahmad; Ghavanloo, Esmaeal

doi:10.1016/j.physe.2012.04.007

Cited by 44 publications

(19 citation statements)

References 27 publications

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“…Eringen s nonlocal theory and Timoshenko beam theory were used to make a buckling analysis of SWCNT on elastic medium [13,14]. Non-conservative dynamic of nonlocal cantilever carbon nanotubes (CNTs) on viscoelastic medium is proposed [15]. Mikhasev [16] researched localized modes of free vibrations of SWCNT.…”

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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“…The relative relation between transverse deflection and reaction pressure of standard linear solid viscoPasternak medium can be defined as [24] 1…”

Section: Surface Elasticity Modelmentioning

confidence: 99%

“…Finite element method has been used to investigate the influence of the Kelvin-Voigt viscoelastic medium on the in-plane vibration of curved carbon nanotubes by Ghavanloo et al [23]. All three models of viscoelastic foundation (Kelvin-Voigt model, Maxwell model and standard linear solid model) were applied by KazemiLari et al [24] to model the interaction between cantilever carbon nanotube and surrounding viscoelastic medium. The authors applied the Galerkin approach to convert the partial differential governing equation into a set of eigenvalue equations.…”

Section: Introductionmentioning

confidence: 99%

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

2016

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In this study, nonlocal elasticity theory in conjunction with Gurtin-Murdoch elasticity theory is employed to investigate biaxial buckling and free vibration behavior of nanoplate made of functionally graded material (FGM) and resting on a viscoPasternak standard linear solid-type of the foundation. The material characteristics of simply supported FGM nanoplates are assumed to be varied continuously as a power law function of the plate thickness. Hamilton's principle is implemented to derive the non-classical governing equations of motion and related boundary conditions, which analytically solved to obtain the explicit closed-form expression for complex natural frequencies and buckling loads. Finally, attention is focused on considering the influences of various parameters on variation of damped natural frequency and buckling load ratio such as nonlocal parameter, surface effects, geometric parameters, power law index and properties of visco-Pasternak foundation and it is clearly demonstrated that these factors highly affect on vibration and buckling behavior.

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“…It is thus important to study the mechanical properties of CNTs [10]. Specially, the vibration characteristics of CNTs resting on a foundation [11][12][13][14][15] plays a crucial role in facilitating the development of nano/micro-sensors [16], fluid storages, and nanocomposites [17], etc. It thus becomes a major topic of great interest in recent research of nanomechanics.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation

et al. 2017

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Vibration responses are investigated for a viscoelastic single-walled carbon nanotube (visco-SWCNT) resting on a viscoelastic foundation. Based on the nonlocal Euler-Bernoulli beam model, velocity-dependent external damping and Kelvin viscoelastic foundation model, the governing equations are derived. The transfer function method (TFM) is then used to compute the natural frequencies for general boundary conditions and foundations. In particular, the exact analytical expressions of both complex natural frequencies and critical viscoelastic parameters are obtained for the Kelvin-Voigt visco-SWCNTs with full foundations and certain boundary conditions, and several physically intuitive special cases are discussed. Substantial nonlocal effect, the influence of geometric and physical parameters of the SWCNT and the viscoelastic foundation are observed for the natural frequencies of the supported SWCNTs. The study demonstrates the efficiency and robustness of the developed model for the vibration of the visco-SWCNT-viscoelastic foundation coupling system.

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Non-conservative instability of cantilever carbon nanotubes resting on viscoelastic foundation

Cited by 44 publications

References 27 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

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation

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