Nonlinear vibration of coupled nano- and microstructures conveying fluid based on Timoshenko beam model under two-dimensional magnetic field

Arani, A. Ghorbanpour; Dashti, P.; Amir, Saeed; Yousefi, M.

doi:10.1007/s00707-015-1342-2

Cited by 29 publications

(7 citation statements)

References 38 publications

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“…The kinetic energy of the nanotube is obtained according to equation (15) (GhorbanpourArani et al , 2015): …”

Section: Governing Dynamic Equationsmentioning

confidence: 99%

“…where the virtual work of centripetal force is obtained according to equation (24) (GhorbanpourArani et al , 2015): …”

Section: Governing Dynamic Equationsmentioning

confidence: 99%

“…and the virtual work of viscous force is obtained according to equation (25) (GhorbanpourArani et al , 2015): where Af is the area through which the fluid passes.…”

Section: Governing Dynamic Equationsmentioning

confidence: 99%

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Numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid

Mohamadi

Eftekhari

Toghraie

2019

HFF

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Purpose The purpose of this paper is to investigate nonlinear vibrations of triple-walled carbon nanotubes buried within Pasternak foundation carrying viscous fluids. Design/methodology/approach Considering the geometry of nanotubes, the governing equations were initially derived using Timoshenko and modified couple stress theories and by taking into account Von-Karman expressions. Then, by determining boundary conditions, type of fluid motion, Knudsen number and, ultimately, fluid viscosity, the principal equation was solved using differential quadrature method, and linear and nonlinear nanotube frequencies were calculated. Findings The results indicated that natural frequency is decreased as the fluid velocity and aspect ratio increase. Moreover, as the aspect ratio is increased, the results converge for simple and fixed support boundary conditions, and the ratio of nonlinear to linear frequencies approaches. Natural frequency of vibrations and critical velocity increase as Pasternak coefficient and characteristic length increase. As indicated by the results, by assuming a non-uniform velocity for the fluid and a slip boundary condition at Kn = 0.05, reductions of 10.714 and 28.714% were observed in the critical velocity, respectively. Moreover, the ratio of nonlinear to linear base frequencies decreases as the Winkler and Pasternak coefficients, maximum deflection of the first wall and characteristic length are increased in couple stress theory. Originality/value This paper is a numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid.

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“…The kinetic energy of the nanotube is obtained according to equation (15) (GhorbanpourArani et al , 2015): …”

Section: Governing Dynamic Equationsmentioning

confidence: 99%

“…where the virtual work of centripetal force is obtained according to equation (24) (GhorbanpourArani et al , 2015): …”

Section: Governing Dynamic Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid

Mohamadi

Eftekhari

Toghraie

2019

HFF

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“…On the basis of classical EB beam model, Ghavanloo et al 34 analyzed instability and free vibrations of conveying fluid CNTs resting on the viscoelastic Winkler foundation. According to the nonlocal and modified couple stress theories, Ghorbanpour Arani et al 35 presented a numerical study on the large-amplitude vibrations of viscoelastic CNTs conveying viscous fluid under magnetic field. Ghavanloo and Fazelzadeh 36 studied the flexural vibration of viscoelastic CNTs conveying fluid and embedded in viscous fluid in the context of the nonlocal first-order shear-deformable beam model.…”

Section: Introductionmentioning

confidence: 99%

Investigating vibrations of viscoelastic fluid-conveying carbon nanotubes resting on viscoelastic foundation using a nonlocal fractional Timoshenko beam model

Oskouie

Ansari

Rouhi

2020

Proceedings of the Institution of Mechanical Engineers, Part N:

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On the basis of fractional viscoelasticity, the size-dependent free-vibration response of viscoelastic carbon nanotubes conveying fluid and resting on viscoelastic foundation is studied in this article. To this end, a nonlocal Timoshenko beam model is developed in the context of fractional calculus. Hamilton’s principle is applied in order to obtain the fractional governing equations including nanoscale effects. The Kelvin–Voigt viscoelastic model is also used for the constitutive equations. The free-vibration problem is solved using two methods. In the first method, which is limited to the simply supported boundary conditions, the Galerkin technique is employed for discretizing the spatial variables and reducing the governing equations to a set of ordinary differential equations on the time domain. Then, the Duffing-type time-dependent equations including fractional derivatives are solved via fractional integrator transfer functions. In the second method, which can be utilized for carbon nanotubes with different types of boundary conditions, the generalized differential quadrature technique is used for discretizing the governing equations on spatial grids, whereas the finite difference technique is used on the time domain. In the results, the influences of nonlocality, geometrical parameters, fractional derivative orders, viscoelastic foundation, and fluid flow velocity on the time responses of carbon nanotubes are analyzed.

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“…As part of the numerous applications, carbon nanotube (CNT) has been used for conveying/transporting fluid and the study of effects and the conditions of moving fluid on the overall mechanical behaviour of CNTs have been an area that has aroused significant and challenging research interests. Consequently, the dynamic analysis of flow-induced vibration of CNT has attracted a large number of studies in literatures in recent years [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Modeling the dynamic behaviours of the structures under the influence of some thermo-fluidic or thermo-mechanical parameters often results in nonlinear equations and such are difficult to find the exact analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

Thermo-Fluidic Parameters Effects on Nonlinear Vibration of Fluid-Conveying Nanotube Resting on Elastic Foundations Using Homotopy Perturbation Method

Sobamowo¹

2018

Journal of Thermal Engineering

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In this paper, effects of thermo-fluidic parameters on the nonlinear dynamic behaviours of single-walled carbon nanotube conveying fluid with slip boundary conditions and resting on linear and nonlinear elastic foundations under external applied tension and global pressure is studied using homotopy perturbation method. From the result, it is observed that increase in the Knudsen number, the slip parameter, leads to decrease in the frequency of vibration and the critical velocity while natural frequency and the critical fluid velocity increase as the in stretching effect increases. Also, as the Knudsen number increases, the bending stiffness of the nanotube decreases and in consequent, the critical continuum flow velocity decreases as the curves shift to the lowest frequency zone. As the change in temperature increases, the natural frequencies and the critical flow velocity of the structure increase for the low or room temperature while at high temperature, increase in temperature change, decreases the natural frequencies and the critical flow velocity of the structure. Further, it is established that the alteration of nonlinear flow-induced frequency from linear frequency is significant as the amplitude, flow velocity and axial tension increase. The developed analytical solutions can be used as starting points for better understanding of the relationship between the physical quantities of the problem.

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Nonlinear vibration of coupled nano- and microstructures conveying fluid based on Timoshenko beam model under two-dimensional magnetic field

Cited by 29 publications

References 38 publications

Numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid

Numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid

Investigating vibrations of viscoelastic fluid-conveying carbon nanotubes resting on viscoelastic foundation using a nonlocal fractional Timoshenko beam model

Thermo-Fluidic Parameters Effects on Nonlinear Vibration of Fluid-Conveying Nanotube Resting on Elastic Foundations Using Homotopy Perturbation Method

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