Stress and strain-inertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory

Daneshmand, Farhang; Rafiei, M.; Mohebpour, Saeed Reza; Heshmati, M.

doi:10.1016/j.apm.2013.01.052

Cited by 34 publications

(10 citation statements)

References 25 publications

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“…Experiment has indicated that the mechanical behavior of mirco-and nano-structures are highly size dependent [35,36]. For instance, the torsional hardening of copper wire increases by a factor of 3 as the wire diameter decreases from 170 to 12 µm [37].…”

Section: Fundamentals Of Strain Gradient Theorymentioning

confidence: 98%

Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow

Sedighi

Koochi

Daneshmand

et al. 2015

International Journal of Non-Linear Mechanics

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Section: Fundamentals Of Strain Gradient Theorymentioning

confidence: 98%

Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow

Sedighi

Koochi

Daneshmand

et al. 2015

International Journal of Non-Linear Mechanics

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“…It is further assumed that the relative displacement u α is small compared to the doublet separation distance η α (| u α | η α ) whereby it may be concluded that the unit vector τ α = τ 0 α [21]. The extensional microstrain scalar measure ε α , representing the axial deformation of the doublet vector, is defined as [29]:…”

Section: Brief Review Of Dmmentioning

confidence: 99%

“…Theory of continuum mechanics is used to develop the equations of motion whereas the small scale effects due to atomic scale of the lattice structures of CNTs are not taken into account. Moreover, the length scales associated with nanotubes are often sufficiently small to call the applicability of classical continuum models into question [21]. Classical continuum mechanics modelling assumptions are conducive to erroneous results, when applied to material domains especially where the typical microstructural dimension is comparable with the structural ones [22].…”

Section: Introductionmentioning

confidence: 99%

A new method for evaluating the natural frequency in radial breathing like mode vibration of double‐walled carbon nanotubes

Fatahi-Vajari

2017

Z Angew Math Mech

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This paper investigates the radial breathing like mode (RBLM) vibration of double-walled carbon nanotubes (DWCNTs) based on a new theory called doublet mechanics (DM) with a scale parameter. To this end, DWCNTs are considered as two concentric elastic thin cylindrical shells bounded together with van der Waals (vdW) forces between them. The vdW forces are modeled using Len-Jones potential. Using DM, two coupled second order partial differential equations that govern the RBLM vibration of DWCNTs are derived. Subsequently, the equations of motion are solved to obtain the natural frequencies in the RBLM vibration. It is the first time that DM is used to derive the natural frequencies of the RBLM vibration for DWCNTs. The advantage of these analytical formulas is that unlike the other methods, they are explicitly dependent to scale parameter and chirality effect. It is shown that the chirality and scale parameter play significant role in the RBLM vibration response of DWCNTs. To validate the accuracy and efficiency of this work, the results obtained herein are compared with the existing theoretical and experimental results and good agreement is observed.

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“…Actuated MEMS/NEMS devices are widely utilized in inkjet printers, switches, gyroscopes, chemo-sensors, micro-manipulators and so on. Recently, several numerical and experimental studies have been conducted on the pull-in instability, static and dynamic behavior of MEMS/NEMS devices [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Vibrations of electrostatically actuated microbeams have been analyzed by Batra et al [1].…”

Section: Introductionmentioning

confidence: 99%

Modeling of Surface Stress Effects on the Dynamic Behavior of Actuated Non-Classical Nano-Bridges

Sedighi

2015

Transactions of the Canadian Society for Mechanical Engineering

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The influence of surface stress and small scale on the dynamic pull-in behavior of nano-bridges is investigated in this paper. For this purpose, the governing equation of motion is derived based on the modified couple stress theory and Homotopy Perturbation Method with an auxiliary term is employed to produce the approximate solution of nano-beam vibrations. The effects of actuation voltage, initial conditions, surface energy and length scale parameter on the pull-in instability and fundamental frequency of the system are studied. The accuracy of proposed asymptotic approach is validated with numerical simulations. The obtained results from asymptotic analysis reveal that two terms in series expansions are sufficient to produce an acceptable approximation. The nano-actuator dynamics exhibit periodic and homoclinic orbits.

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Stress and strain-inertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory

Cited by 34 publications

References 25 publications

Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow

Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow

A new method for evaluating the natural frequency in radial breathing like mode vibration of double‐walled carbon nanotubes

Modeling of Surface Stress Effects on the Dynamic Behavior of Actuated Non-Classical Nano-Bridges

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