Torsional buckling of a DWCNT embedded on winkler and pasternak foundations using nonlocal theory

Mohammadimehr, Mehdi; Saidi, A.R.; Arani, A. Ghorbanpour; Arefmanesh, A.; Han, Qiang

doi:10.1007/s12206-010-0331-6

Cited by 51 publications

(22 citation statements)

References 22 publications

(32 reference statements)

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“…The mechanical properties of a DWCNT, the surrounding elastic medium and the small scale effect can be considered as follows (Refs. [9,11,13] Variation of phase velocity versus axial half wave number for different wave modes obtained from local and nonlocal theories are shown in Figs. 2 and 3 respectively.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

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Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory

et al. 2011

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The axial and torsional wave propagation in a double-walled carbon nanotube (DWCNT) embedded on elastic foundations are investigated using nonlocal continuum shell theory. The effects of the surrounding elastic medium are considered using the spring constant of the Winkler-type and the shear constant of the Pasternak-type. The van der Waals (vdW) forces between the inner and the outer nanotubes are taken into account. The dynamic response of the carbon nanotube is formulated on the basis of nonlocal elasticity shell theory. The cut-off frequencies are obtained and it has been concluded that the cut-off frequencies are independent of small scale coefficient and shear modulus of the elastic medium. It has been found that the phase velocity sharply decreases by increasing the axial half wave number and approaches a constant value. It has also been concluded that the maximum phase velocity predicted by nonlocal theory is located between 5 and 10 nanometers while for local theories the phase velocity sharply decreases in this interval and approaches a constant value. Results show that the effect of Pasternak-type on phase velocity is significant but the effect of Winkler-type is not really considerable.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

“…(9) and ignoring , , , tt tt u v , the governing equations of motion can be written as r , the outer radius 2 r , length L , thickness h . For the outer tube which is denoted by subscript "1", the normal pressure 1 p can be considered as [11] …”

Section: Governing Equations Of Motion For a Dwcnt Using The Nonlocalmentioning

confidence: 99%

Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory

et al. 2011

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“…(20), (23) and (24), and the governing equations of motion for viscoelastic tapered micro-rod based on strain gradient theory are obtained as follows: …”

Section: Vibration Of Viscoelastic Tapered Microrodmentioning

confidence: 99%

“…Their results indicated that the axial displacement of SWBNNRs increases with an increase in the temperature change and also, for the piezoelectric coefficient, it is the same. Mohammadimehr et al [20] carried out torsional buckling of double-walled carbon nanotubes (DWCNT) on Winkler and Pasternak foundations using nonlocal elasticity theory. It is shown from their results that the nonlocal critical buckling load is lower than the local critical buckling load.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM

2015

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In the present work, based on strain gradient theory, the free vibration analysis of tapered viscoelastic micro-rod resting on viscoPasternak foundation is investigated. The material properties of micro-rod are assumed the visco-elastic and modeled as the Kelvin-Voigt. Using Hamilton's principle and energy method, the governing equation of motion of viscoelastic micro-rods is derived, then this obtained equation using the differential quadrature method (DQM) for different boundary conditions is solved. In this study, the effects of various parameters such as the structural damping coefficient, Winkler and Pasternak foundation modulli, damping coefficient of the elastic medium and material length scale parameters on the non-dimensional natural frequencies of viscoelastic micro-rod are investigated. The results show that with an increase in the Winkler and Pasternak coefficients, the natural frequency increases as well as the obtained nondimensional natural frequencies by MCST and SGT decrease by increasing the material length to radius ratio. It can be seen that the nondimensional frequency for SGT is higher than that of the other theories. It is shown that the non-dimensional frequencies increase by increasing the damping coefficient for all theories. Moreover, at the specified value of damping coefficient of the elastic medium, the variation of non-dimensional natural frequency is approximately smooth.

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“…In this work, different nonlocal beam models corresponding to the different classical beam theories [22][23][24] are presented on the basis of Eringen's equations of nonlocal elasticity [25] to predict the buckling behavior of nanobeams with four commonly used boundary conditions. State-space method is used to solve the governing differential equations for each type of nonlocal beam model with different boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions

Sahmani

Ansari

2011

J Mech Sci Technol

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Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen's equations of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary conditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analysis of nanobeams relevant to each type of nonlocal beam model and boundary conditions.analysis.

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Torsional buckling of a DWCNT embedded on winkler and pasternak foundations using nonlocal theory

Cited by 51 publications

References 22 publications

Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory

Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory

Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM

Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions

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