Free and forced axial vibration of single walled carbon nanotube under linear and harmonic concentrated forces based on nonlocal theory

2020 ◽  
Vol 34 (08) ◽  
pp. 2050067 ◽  
Author(s):  
Farshad Khosravi ◽  
Seyyed Amirhosein Hosseini ◽  
Hasti Hayati
Keyword(s):  
Carbon Nanotube ◽  
Natural Frequencies ◽  
Constitutive Relations ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Axial Vibration ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Concentrated Forces

The aim of this paper is to investigate the free and forced axial vibrations under the two various linear and harmonic axial concentrated forces in zigzag single-walled carbon nanotube (SWCNT). Two different boundary conditions, namely clamped–clamped and clamped-free, are established. Eringen’s nonlocal elasticity is employed to justify the nonlocal behavior of constitutive relations. The governing equation and the associated boundary condition are derived based on Hamilton’s principle. In order to solve the derived equation numerically, the assumed modes method is utilized. In the free axial vibration section, the first three natural frequencies are obtained for the various values of the nonlocal parameter. The results are in good agreement in comparison with another study. The fundamental natural frequencies with respect to the nonlocal parameter of the case study as a semiconducting nanotube with boron nitride nanotube (BNNT) as a semiconducting nanotube and SWCNT (5,5) as a metallic nanotube are compared. The effects of the nonlocal parameter, thickness and ratio of the excitation-to-natural frequencies overtime on dimensional and nondimensional axial displacements are studied.

NONLINEAR VIBRATION AND BENDING INSTABILITY OF A SINGLE-WALLED CARBON NANOTUBE USING NONLOCAL ELASTIC BEAM THEORY

2011 ◽  
Vol 10 (03) ◽  
pp. 447-453 ◽  
Author(s):  
I. MEHDIPOUR ◽  
P. SOLTANI ◽  
D. D. GANJI ◽  
A. FARSHIDIANFAR
Keyword(s):  
Carbon Nanotube ◽  
Nonlocal Parameter ◽  
Elastic Beam ◽  
Beam Theory ◽  
Special Kind ◽  
Nonlocal Theory ◽  
Length Ratio ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Bending Modulus

Due to the nonlocal Euler–Bernoulli elastic beam theory, the effects of rippling deformation on the bending modulus and the structural bending instability of a single-walled carbon nanotube (SWCNT) are investigated. The nonlinear vibrational model of a cantilevered SWCNT is solved using the perturbation method of multiscales. The nonlinear resonant frequency and the associated effective bending modulus of the carbon nanotube (CNT) are derived analytically. The effects of the nonlocal parameter, the external harmonic force, and the diameter-to-length ratio on the effective bending modulus are discussed widely. Moreover, the model can predict special kind of structural instability due to the rippling deformation called rippling instability. The results show that the nonlocal theory forecasts larger values for the effective bending modulus compared with the classical beam theory, especially for the stubby CNTs. Meanwhile, the rippling instability threshold will move to the higher values of the diameter-to-length ratio based on the nonlocal beam theory comparing with the local ones.

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

2020 ◽  
Vol 63 ◽  
pp. 112-133 ◽  
Author(s):  
Farshad Khosravi ◽  
Seyyed Amirhosein Hosseini ◽  
Abdelouahed Tounsi
Keyword(s):  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Elastic Medium ◽  
Time Domain ◽  
Natural Frequencies ◽  
Moving Load ◽  
Nonlocal Parameter ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
The Time Domain

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.

Size-dependent free vibration of axially functionally graded tapered nanorods having nonlinear spring constraint with a tip nanoparticle

2019 ◽  
Vol 25 (21-22) ◽  
pp. 2769-2783 ◽  
Author(s):  
Arian Bahrami ◽  
Ali Zargaripoor ◽  
Hamidreza Shiri ◽  
Nima Khosravi
Keyword(s):  
Literature Review ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Functionally Graded ◽  
The Other ◽  
Constant Mass ◽  
Axial Vibration ◽  
Nonlinear Spring ◽  
Size Dependent

According to the present literature review, the axial vibration of the axially functionally graded (FG) tapered nanorod with attached nonlinear spring has not been addressed so far. In this study, the axial vibration of the FG tapered nanorod is studied based on Eringen’s nonlocal theory, in which one end of the nanorod is clamped and the other end is attached to a nonlinear spring and a nanoparticle. The influence of different parameters such as the nonlinear spring constant, mass of the nanoparticle, and the nonlocal parameter on the natural frequencies is presented in detail. The solutions via Tables can be utilized as a reliable reference for evaluating the validity of future researches. The presented nonlocal solutions can be helpful for those who are interested in designing micro/nano electromechanical systems.

Nonlinear Vibration Analysis of Single-Walled Carbon Nanotube With Shell Model Based on the Nonlocal Elasticity Theory

2016 ◽  
Vol 11 (1) ◽  
Author(s):  
P. Soltani ◽  
J. Saberian ◽  
R. Bahramian
Keyword(s):  
Carbon Nanotube ◽  
Differential Equations ◽  
Nonlinear Vibration ◽  
Nonlocal Elasticity ◽  
Geometrical Nonlinearity ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Aspect Ratios

In this paper, nonlinear vibration of a single-walled carbon nanotube (SWCNT) with simply supported ends is investigated based on von Karman's geometric nonlinearity and nonlocal shell theory. The SWCNT is designated as an individual shell, and the Donnell's formulations of a cylindrical shell are used to obtain the governing equations. The Galerkin's procedure is used to discretized partial differential equations (PDEs) into the ordinary differential equations (ODEs) of motion, and the method of averaging is applied to obtain an analytical solution of the nonlinear vibration of (10,0), (20,0), and (30,0) zigzag SWCNTs. The effects of the nonlocal parameters, nonlinear parameters, different aspect ratios, and different circumferential wave numbers are investigated. The results of the classical and the nonlocal models are compared with different nonlocal elasticity constants (e0a). It is shown that the nonlocal parameter predicts different resonant frequencies in comparison to the local models. The softening and/or hardening nonlinear behaviors of the CNTs may change against the nonlocal parameters. Hence, considering the geometrical nonlinearity and the nonlocal elasticity effects, the dynamical models of the SWCNTs predict their vibration behaviors accurately and should not be ignored during theoretical modeling.

scholarly journals Effect of Power Law-Index for Accurate Natural Frequencies of Rotating Isotropic SWCNTs with Ring Supports

2019 ◽  
Author(s):  
Muzamal Hussain ◽  
Muhammad Nawaz Naeem
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Current Model ◽  
Angular Speed ◽  
Radius Ratio ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Love’S Shell Theory

Vibration analysis of carbon nanotubes (CNTs) is very essential field owing to their many promising applications in tiny instruments. The unique and interesting properties of CNTs, particularly their mechanical and electrical features, have fascinated industries and researchers to implement CNTs for production of different electromechanical devices. Research on vibration behavior of CNTs was done for a few decades ago. Vibrations of isotropic rotating zigzag and chiral single-walled carbon nanotube (SWCNTs) with ring supports are established using the Love’s shell theory. To discretize the governing equations of current model, Galerkin’s method is utilized for frequency equations of single-walled carbon nanotubes (SWCNTs). The unknown axial functions have assumed by characteristic beam functions which fulfill boundary conditions applied at the tube ends. Effects of different parameters with ring supports on the fundamental natural frequencies versus ratio of length-to-radius, angular speed and height-to-radius ratio have been investigated. The frequencies curves decrease as the length-to-diameter ratio increases. With the increase of angular speed the frequency curve of backward waves increases and forward wave decreases for rotating zigzag and chiral tubes. On the other hand, the phenomena of frequency versus height-to-radius ratio are counterpart of length-to-radius ratio for rotating boundary conditions. The frequency phenomena have been observed very pronounced with ring support. Frequency value of C-C end condition is higher than those of C-F computations. The results of single-walled carbon nanotube are computed by using MATLAB software. To validate the accuracy of present model, the results have been compared with earlier modeling/simulations.

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