Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen’s theory using differential quadrature method

Ghadiri, Majid; Shafiei, Navvab

doi:10.1007/s00542-015-2662-9

Cited by 74 publications

(20 citation statements)

References 41 publications

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“…Now equations of motion and boundary conditions can be obtained by substituting Eqs. (6), (8), (9), (13), (17) and (18) into (4) and integrating by parts.…”

Section: Governing Equations Of Motion and Corresponding Boundary Conmentioning

confidence: 99%

“…Nonlocal elasticity theory expresses the stress field at a reference point that is assumed to be dependent on the strains at all points in the body, not only at the reference point [13]. Many vibrational studies [14][15][16][17][18] have paid attention to nonlocal effects using nonlocal elasticity theory. Lee et al [19] employed nonlocal elasticity theory to analyze the effects of flow velocity on the vibration frequency and mode shapes of the single-walled carbon nanotube conveying fluid flow.…”

Section: Introductionmentioning

confidence: 99%

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Effect of distributed axial loading on dynamic stability and buckling analysis of a viscoelastic DWCNT conveying viscous fluid flow

Mohammadi

Barouti

Safarpour

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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In this article, dynamic stability and buckling analysis of a double-walled carbon nanotube (DWCNT) under distributed axial force are investigated. The visco-Pasternak model is used to simulate the elastic medium between nanotubes considering the effects of spring, shear and damping of the elastic medium. This system is conveying viscous fluid, and the relevant force is calculated by modified Navier-Stokes relation considering slip boundary condition and Knudsen number. The nanostructure is modeled as two orthotropic moderately thick cylindrical shells, and the effects of small-scale and structural damping are accounted based on modified couple stress and Kelvin-Voigt theories. The governing equations and boundary conditions are developed using Hamilton's principle and solved with the aid of Navier and generalized differential quadrature methods. In this research, the dynamic instability occurs in the viscoelastic DWCNT conveying viscous fluid flow as the natural frequency becomes equal to zero. The results show that the velocity of viscous fluid flow, axial load, mode number, length-to-radius ratio, radius-to-thickness ratio, visco-Pasternak foundation and the boundary conditions play important roles on the critical pressure and natural frequency of the viscoelastic DWCNT conveying viscous fluid flow under axial force.

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“…Now equations of motion and boundary conditions can be obtained by substituting Eqs. (6), (8), (9), (13), (17) and (18) into (4) and integrating by parts.…”

Section: Governing Equations Of Motion and Corresponding Boundary Conmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of distributed axial loading on dynamic stability and buckling analysis of a viscoelastic DWCNT conveying viscous fluid flow

Mohammadi

Barouti

Safarpour

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Such structures have been modeled and studied experimentally as rotary nano‐motors with controlled ultrahigh speed, which are applied for controlled biochemical release and demonstrate releasing rate of biochemicals on nanoparticles that can be precisely tuned by mechanical rotations 12 . Rotary effect of nanostructures is of great importance to study, and a lot of researchers have performed analysis on rotating beams 13–17 . Aranda‐Ruiz et al 18 derived the natural frequencies of the flapwise bending vibrations of a nonuniform rotating cantilever nano‐beam considering the rotational force.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of rotating double‐tapered cantilever Timoshenko nano‐beam using the nonlocal strain gradient theory

2020

Math Methods in App Sciences

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Based on the nonlocal strain gradient theory, the coupling nonlinear dynamic equations of a rotating double‐tapered cantilever Timoshenko nano‐beam are derived using the Hamilton principle. The equation of motion is discretized via the differential quadrature method. The effects of the angular velocity, nonlocal parameter, slenderness ratio, cross‐section parameter, and taper ratios are examined and discussed. It is shown that taper ratios and cross‐section parameter play a significant role in the vibration response of a rotating cantilever nano‐beam. Further as rotational angular velocity increases, the taper ratios and cross‐section parameter effect on the frequency response are increased for first modes of vibration.

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“…Employing EBT and differential transform method, Ghafarian and Ariaei 48 studied the free flapping vibration characteristics of elastically connected multiple rotating nano-beams. Using EBT and DQM, non-linear free vibrations of cantilever and propped cantilever rotating nano-beams for flapping modes were studied by Ghadiri and Shafiei, 49 and by Shafiei et al 50 considering thermal effect. Employing Timoshenko beam theory (TBT) and DQM, Azimi et al 51,52 studied free flapping vibration behavior of cantilever and propped cantilever rotating FGM nano-beams with material gradation either across the length or across the thickness directions and subjected to thermal loading.…”

Section: Introductionmentioning

confidence: 99%

Study on free vibration behavior of rotating bidirectional functionally graded nano-beams based on Eringen’s nonlocal theory

Malik

Das

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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Free vibration behavior of rotating bidirectional functionally graded nano-beams is studied based on Eringen’s nonlocal theory. The beam material consists of ceramic and metal constituents, and the material is graded across the length and thickness directions. The mathematical formulation is framed on Euler–Bernoulli beam theory, and the system of governing equations is derived in variational form using Hamilton’s principle. The governing equations are discretized and transformed to an eigen value problem using Ritz method. The model is formulated to study the flapping and lead-lag motions due to free vibration. The model is verified with the available numerical results. The numerical results are presented in non-dimensional frequency-speed plane to study the influence of normalized nonlocal parameter, length gradient parameter, thickness gradient parameter, root radius parameter, and section aspect ratio. Some normalized mode shapes are presented to illustrate the mode switching phenomenon. The mathematical model of a nonlocal rotating bidirectional functionally graded material nano-beam is presented for the first time through this work and the reported results are new of its kind.

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Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen’s theory using differential quadrature method

Cited by 74 publications

References 41 publications

Effect of distributed axial loading on dynamic stability and buckling analysis of a viscoelastic DWCNT conveying viscous fluid flow

Effect of distributed axial loading on dynamic stability and buckling analysis of a viscoelastic DWCNT conveying viscous fluid flow

Dynamic analysis of rotating double‐tapered cantilever Timoshenko nano‐beam using the nonlocal strain gradient theory

Study on free vibration behavior of rotating bidirectional functionally graded nano-beams based on Eringen’s nonlocal theory

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