Torsional vibration of cracked carbon nanotubes with torsional restraints using Eringen’s nonlocal differential model

Yaylı, Mustafa Özgür; Kandemir, Süheyla Yerel; Çerçevik, Ali Erdem

doi:10.1177/1461348418813255

Cited by 13 publications

(10 citation statements)

References 64 publications

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“…A verification study is needed to show the accuracy of the Rayleigh-Ritz method used by this investigation. Table 1 shows the results of the present study and those obtained by Yayli et al [44] and the finite elements method (FEM) of Numanoğlu and Civalek [47]. As it is obvious, the present study results are in a good agreement with the results of the indicated references.…”

Section: Validation Studysupporting

confidence: 84%

“…Murmu et al [43] applied the nonlocal elasticity approach to study the torsional vibration of carbon nanotube-buckyball systems. Effect of the cracks on the torsional vibration of carbon nanotubes with torsional restraints using Eringen's nonlocal differential model has been investigated by [44]. Based on nonlocal elasticity theory, Zarezadeh et.…”

Section: Introductionmentioning

confidence: 99%

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Temperature change effect on torsional vibration of nanorods embedded in an elastic medium using Rayleigh–Ritz method

Abdullah

Hosseini-Hashemi

Hussein

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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This paper studies torsional vibration of carbon nanotubes/nanorods embedded in an elastic medium under thermal stresses. Nonlocal theory is applied to the nanorod equations. The thermal stresses act in axial and other directions, and their amounts vary as temperature changes. The elastic medium is modeled as a rotational spring around the nanorod. Hamilton's principle is used to obtain motion equation. Rayleigh-Ritz method is used to solve the differential equation of motion. Effect of nonlocal scale coefficient, low and high temperatures, elastic medium stiffness, and nanorod diameter and length is investigated. Influence of temperature on the frequencies depends on the values of stiffness of elastic medium, and nanotube diameter and length.

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Section: Validation Studysupporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Temperature change effect on torsional vibration of nanorods embedded in an elastic medium using Rayleigh–Ritz method

Abdullah

Hosseini-Hashemi

Hussein

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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“…Yayli [25] and Huang [26] investigated the torsional vibrations of restrained nanotubes subjected to constraint of surface elasticity. Taking the effect of nonlocal strain, Yayli et al [27] investigated the effects of torsional restraints on the vibration of cracked carbon nanotubes. Khosravi et al [28] analyzed the torsional vibrations of nanowire.…”

Section: Introductionmentioning

confidence: 99%

Torsional Wave in a Dissipative Cylindrical Shell Under Initial Stresses

Selim¹,

Gepreel²

2022

Computers, Materials &Amp; Continua

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The dispersion relation of torsional wave in a dissipative, incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated. The governing equation and closed form solutions are derived with the aid of Biot's principle. Phase velocity and damping of torsional wave are obtained analytically and the influences of dissipation and initial stresses are studied in details. We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form. Numerical results analyzing the torsional wave propagation incorporating initial stress effects are analyzed and presented in graphs. The analytical and numerical solutions reveal that, the dissipation as well as the initial stresses have notable impacts on the phase velocity of torsional wave in a pre-stressed dissipative cylindrical shell. The numerical results reveal that, the initial stresses and dissipation, considerably, effect the phase velocity of the torsional wave. It has been observed that, any change in dissipation parameter (δ) produces a substantial change in damping velocity of torsional wave. In addition, it can be seen that, the phase velocity increases as the initial stress parameter increases. Finally, the result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation. The conclusion made shown the consistency with the Biot's incremental deformation theory, and the effective on model such as engineering mechanics and displacement of particles.

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“…Gulevsky et al (2018) researched torsional vibrations of shafts of mechanical systems to compare the calculated dependencies for determining the equivalent rigidity of the mechanical systems and to come to an agreement on the methods of compiling dynamic models for systems with elastic reducer couplings in applied and classical oscillation theories. Nageswaranath et al (2020) presented effect of imperfect bonding on torsional vibrations of composite poroelastic cylinders; Yan et al (2019) proposed a coupling atomisticcontinuum model with Euler beam theory and capturing the size effect to investigate longitudinal and torsional free vibration characteristics of boron nitride nanotubes with both cantilevered and clamped constraints; Setoodeh et al (2016) analytically studied linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory; Yayli et al (2019) discussed torsional vibration of cracked carbon nanotubes with elastic torsional boundary conditions using Eringen's nonlocal differential model; Khosravi et al (2020) gave analytical investigation on free torsional vibrations of noncircular nanorods containing noncircular cross sections; Li (2014) investigated differences of torsional vibration of carbon nanotubes between two nonlocal models and a semicontinuum model. In these studies, the structures are made of linear elasticity materials and linear shear stress-strain constitutive relationships are adopted to study the free torsional vibrations of the structures.…”

Section: Introductionmentioning

confidence: 99%

“…(2019) proposed a coupling atomistic-continuum model with Euler beam theory and capturing the size effect to investigate longitudinal and torsional free vibration characteristics of boron nitride nanotubes with both cantilevered and clamped constraints; Setoodeh et al. (2016) analytically studied linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory; Yayli et al. (2019) discussed torsional vibration of cracked carbon nanotubes with elastic torsional boundary conditions using Eringen’s nonlocal differential model; Khosravi et al.…”

Section: Introductionmentioning

confidence: 99%

An indirect method to determine nonlinearly elastic shear stress-strain constitutive relationships for nonlinear torsional vibration of nonlinearly elastic shafts

Fan

Jian-she²,

Xue³

et al. 2022

MMMS

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PurposeIn this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials, and then study the nonlinear free torsional vibration of Al–1%Si shaft.Design/methodology/approachIn this study the authors use BoxLucas1 model to fit the determined-experimentally nonlinear elastic normal stress–strain constitutive relationship curve of Al–1%Si, a typical case of isotropic nonlinear elasticity materials, and then derive its nonlinear shear stress-strain constitutive relationships based on the fitting constitutive relationships and general equations of plane-stress and plane-strain transformation. Hamilton’s principle is utilized to gain nonlinear governing equation and boundary conditions for free torsional vibration of Al–1%Si shaft. Differential quadrature method and an iterative algorithm are employed to numerically solve the gained equations of motion.Findings The effect of four variables, namely dimensionless fundamental vibration amplitude ϑmax, radius α and length β, and nonlinear-elasticity intensity factor δ, on frequencies and mode shapes of the shafts is obtained. Numerical results are in good agreement with reference solutions, and show that compared with linearly elastic shear stress-strain constitutive relationships of the shafts made of the nonlinear elasticity materials, its actual nonlinearly elastic shear stress-strain constitutive relationships have smaller torsion frequencies. In addition, but β having opposite hardening effect, the rest of the four variables have softening effect on nonlinearly elastic torsion frequencies. Eventually, taking into account nonlinearly elastic shear stress-strain constitutive relationships, changes of the four factors, i.e. ϑmax, α, β and δ, cause inflation and deflation behaviors of mode shapes in nonlinear free torsional vibration.Originality/valueThe study could provide a reference for indirectly determining nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials and for structure design of torsional shaft made of nonlinear elasticity materials.

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Torsional vibration of cracked carbon nanotubes with torsional restraints using Eringen’s nonlocal differential model

Cited by 13 publications

References 64 publications

Temperature change effect on torsional vibration of nanorods embedded in an elastic medium using Rayleigh–Ritz method

Temperature change effect on torsional vibration of nanorods embedded in an elastic medium using Rayleigh–Ritz method

Torsional Wave in a Dissipative Cylindrical Shell Under Initial Stresses

An indirect method to determine nonlinearly elastic shear stress-strain constitutive relationships for nonlinear torsional vibration of nonlinearly elastic shafts

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