Torsional dynamic response of viscoelastic SWCNT subjected to linear and harmonic torques with general boundary conditions via Eringen’s nonlocal differential model

The Journal of Strain Analysis for Engineering Design

et al. 2020

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In this article, the free torsional vibration of the noncircular microwire is obtained via modified couple stress theory. The noncircular cross section is considered to be equilateral triangle. The governing equations are derived using Hamilton’s principle, and the natural frequencies of the clamped-clamped and clamped-free microwires are obtained based on a Galerkin method. The natural frequency for analyzing of the results is considered to be dimensionless. The effects of the different parameters including the dimensionless material length scale parameter, the dimensionless edge length of the triangle, and mode number on the dimensionless natural frequency of the microwire are evaluated. Ultimately, the influence of the Poisson’s ratio on the natural frequency of the microwire under various boundary conditions is investigated.

“…Inserting equations (30) and (31) into equation (28) causes the natural frequency of the noncircular microwire based on the modified couple stress theory to be found as…”

Section: Modified Couple Stress Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free torsional vibration of triangle microwire based on modified couple stress theory

Hamidi

The Journal of Strain Analysis for Engineering Design

et al. 2020

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“…There have been done many efforts and studies to develop this theory, such as Refs. [24][25][26][27][28][29][30][31]. Furthermore, there are some studies with different size-dependent theories [32][33].…”

Section: Introductionmentioning

confidence: 99%

Forced Axial Vibration of a Single-Walled Carbon Nanotube Embedded in Elastic Medium under Various Moving Forces

Tounsi

2020

JNanoR

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The dynamic free and forced axial vibrations subjected to moving exponential and harmonic axial forces of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium, are studied in this paper. Two different boundary conditions of SWCNT, including clamped-clamped and clamped-free, are taken into account. Eringen’s nonlocal elasticity theory is used to show the nonlocality for the model. The constitutive equations and their boundary conditions are derived by Hamilton’s principle. Employing the general solution, the derived equations are analytically solved to obtain two items. Firstly, the axial natural frequencies, secondly, the time-domain axial displacements at the middle of the carbon nanotube (CNT), and then the maximum axial displacements. The responses are validated with previous works, and the results demonstrates good agreement to them to verify the influence of the nonlocal parameter on the nondimensional natural frequencies for three various mode numbers. In the time-domain section, the effects of the nonlocal parameter, length, nondimensional stiffness of the elastic medium, and velocity of the moving load on the axial displacement are investigated. Also, the influences of the excitation frequency to natural frequency for the harmonic moving load, as well as the time constant for the exponential moving load on the axial displacement, are illustrated. Finally, the effect of the nonlocal parameter on the maximum axial deflection versus velocity parameter is schematically indicated.

“…The nonlocal Eringen's elasticity theory [15][16][17][18][19] has been established to show the small-scale effect and the torsional behavior of the nanorods. In this way, many studies are devoted to the vibration of the nanostructure via the mentioned nonlocal approach [20][21][22][23][24][25][26][27][28][29][30][31]. Meanwhile, there are some investigations that are carried out via the other theories such as Refs.…”

Section: Introductionmentioning

confidence: 99%

Analytical investigation on free torsional vibrations of noncircular nanorods

J Braz. Soc. Mech. Sci. Eng.

Hamidi

2020

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This paper is devoted to the free torsional behavior of the nanorods containing noncircular cross sections. The rectangular cross section is chosen to be the case of the study. Three various boundary conditions, namely the clamped-clamped (C-C), clamped-free (C-F), and clamped-torsional spring (C-T) boundary conditions, are used to model the nanorod. Hamilton's principle is utilized to derive the equation of motion along with associated boundary conditions. The derived equation is reformulated by Eringen's nonlocal elasticity approach to exhibit the small-scale effect. An analytical method is established to discretize and analyze the equation of motion. The novelty of this work is the analysis of the torsional vibration in rectangular nanorods, which are not observed in previous works. For the results, the influences of the horizontal and vertical aspect ratios ( a∕b and b∕a ) (for C-C and C-F boundary conditions) and the influences of the nonlocal parameter and stiffness of the boundary spring (for C-T boundary condition) are illustrated schematically and tabularly.