Nonlinear Forced Vibration of Carbon Nanotubes Considering Thermal Effects

2014 ◽  
Author(s):  
Hassan Askari ◽  
Ebrahim Esmailzadeh ◽  
Davood Younesian
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Forced Vibration ◽  
Oscillation Amplitude ◽  
Beam Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Winkler Model ◽  
Length Changes ◽  
Nonlinear Forced Vibration ◽  
The Galerkin Method

Nonlinear forced vibration of carbon nanotubes is investigated. The Euler-Bernoulli beam theory in conjunction with Eringen’s theory is considered and the thermal effect is incorporated into the formulation of the governing equation. The Winkler model is assumed for the foundation of carbon nanotube and the Galerkin method is performed to find the nonlinear ordinary differential equation of system based on the assumed boundary conditions. The multiple times scale is applied to investigate the forced vibration of carbon nanotubes. The effect of different parameters, namely, temperature variations and carbon nanotube length changes on the amplitude of oscillation of carbon nanotube are studied. It is found that the linear natural frequency of system increases by increasing the temperature and subsequently, the oscillation amplitude will decrease.

Nonlinear Forced Vibration of Curved Carbon Nanotube Resonators

2016 ◽  
Author(s):  
Hassan Askari ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Carbon Nanotube ◽  
Forced Vibration ◽  
Primary Resonance ◽  
Beam Theory ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Nonlinear Forced Vibration ◽  
Resonator System ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam

Nonlinear forced vibration of the nonlocal curved carbon nanotubes is investigated. The governing equation of vibration of a nonlocal curved carbon nanotube is developed. The nonlinear Winkler and Pasternak type foundations are chosen for the nanotube resonator system. Furthermore, the shape of the carbon nanotube system is assumed to be of a sinusoidal curvature form and different types of the boundary conditions are postulated for the targeted system. The Euler-Bernoulli beam theory in conjunction with the Eringen theory are implemented to obtain the partial differential equation of the system. The Galerkin method is applied to obtain the nonlinear ordinary differential equations of the system. For the sake of obtaining the primary resonance of the considered system the multiple time scales method is utilized. The influences of different parameters, namely, the position of the applied force, different forms of boundary condition, amplitude of curvature, and the coefficient of the Pasternak foundation, on the frequency response of the system were fully investigated.

Nonlinear Vibration of Carbon Nanotube Resonators Considering Higher Modes

2015 ◽  
Author(s):  
Hassan Askari ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Carbon Nanotube ◽  
Multiple Scales ◽  
Beam Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Winkler Foundation ◽  
Bernoulli Beam ◽  
Bernoulli Beam Theory ◽  
Objective System ◽  
Nonlinear Forced Vibration ◽  
Euler Bernoulli Beam

Nonlinear forced vibration of the carbon nanotubes based on the Euler-Bernoulli beam theory is studied. The Euler-Bernoulli beam theory is implemented to find the governing equation of the vibrations of the carbon nanotube. The Pasternak and Nonlinear Winkler foundation is assumed for the objective system. It is supposed that the system is supported by hinged-hinged boundary conditions. The Galerkin procedure is employed in order to find the nonlinear ordinary differential equation of the vibration of the objective system considering two modes of vibrations. The primary and secondary resonant cases are developed for the objective system employing the multiple scales method. Influence of different factors such as length, thickness, position of applied force, Pasternak and Winkler foundation are fully shown on the primary and secondary resonance of the system.

Dynamic Behavior of Carbon Nanotubes Using Nonlocal Rayleigh Beam

2014 ◽  
Author(s):  
Hassan Askari ◽  
Ebrahim Esmailzadeh ◽  
Davood Younesian
Keyword(s):  
Differential Equation ◽  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Forced Vibration ◽  
Multiple Scales ◽  
Surface Effect ◽  
Primary Resonance ◽  
Beam Theory ◽  
Winkler Foundation ◽  
Rayleigh Beam

Forced vibration of carbon nanotubes based on the Rayleigh beam theory in conjunction with Eringen’s nonlocal elasticity is investigated. The governing equation of vibration of carbon nanotube using the above theories is developed. The carbon nanotube is rested on a nonlinear Winkler and Pasternak foundation with the simply-supported boundary conditions. The Gelerkin procedure is utilized to find the nonlinear ordinary differential equation of vibration of system. The differential equation is solved using the multiple scales method in order to investigate the primary resonance of the considered system. The frequency response of the system is obtained and the effects of different parameters, such as the surface effect, position and magnitude of applied force and Pasternak and Winkler foundation, on the vibration behavior of the system are studied. The sensitivity of the amplitude of oscillation of carbon nanotube is depicted with respect to the surface effect. It is shown that the surface effect plays an important role in the forced vibration of the nano-scale structure.

Nonlinear Vibration of Nanobeam With Quadratic Rational Bezier Arc Curvature

2014 ◽  
Author(s):  
Hassan Askari ◽  
Zia Saadatnia ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequency ◽  
Governing Equation ◽  
Oscillation Amplitude ◽  
Beam Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Pasternak Foundation ◽  
Bernoulli Beam ◽  
Linear Frequency ◽  
Euler Bernoulli Beam

Nonlinear vibration of nanobeam with the quadratic rational Bezier arc curvature is investigated. The governing equation of motion of the nanobeam based on the Euler-Bernoulli beam theory is developed. Accordingly, the non-uniform rational B-spline (NURBS) is implemented in order to write the implicit form of the governing equation of the structure. The simply-supported boundary conditions are assumed and the Galerkin procedure is utilized to find the nonlinear ordinary differential equation of the system. The nonlinear natural frequency of the system is found and the effects of different parameters, namely, the waviness amplitude, oscillation amplitude, aspect ratio, curvature shape and the Pasternak foundation coefficient are fully investigated. The hardening and softening responses of the natural frequency of structure are detected for variations of the shape and amplitude of the curvature waviness. It is revealed that the ratio of nonlinear to linear frequency increases with an increase in the oscillation amplitudes. It is found that by increasing the Pasternak foundation coefficient, the ratio of nonlinear to linear frequency decreases.

Nonlinear Forced Vibration Analysis of a Non-Local Carbon Nanotube Carrying Intermediate Mass

2015 ◽  
Author(s):  
Zia Saadatnia ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Carbon Nanotube ◽  
Forced Vibration ◽  
Beam Theory ◽  
Analytical Form ◽  
Harmonic Excitation ◽  
Local Theory ◽  
Mass Detection ◽  
Intermediate Mass ◽  
Non Local ◽  
Forced Vibration Analysis

The aim of this study is to model and investigate the nonlinear transversal vibration of a carbon nanotube carrying an intermediate mass along the structure considering the nonlocal and non-classical theories. Due to the application of the proposed system in sensors, actuators, mass detection units among others, the analysis of forced vibration of such systems is of an important task being considered here. The governing equation of motion is developed by combining the Euler-Bernoulli beam theory and the Eringen non-local theory. The Galerkin approach is employed to obtain the governing differential equation of the system and the transient beam response for the clamped-hinged boundary condition. A strong perturbation method is utilized to solve the equation obtained and the system responses subjected to a harmonic excitation is examined. The steady-state motion is studied and the frequency response in an analytical form is obtained. Finally, results are evaluated for some numerical parameter values and their effect on the frequency responses are presented and fully discussed.

On the forced vibration of carbon nanotubes via a non-local Euler—Bernoulli beam model

2010 ◽  
Vol 224 (2) ◽  
pp. 497-503 ◽  
Author(s):  
P Karaoglu ◽  
M Aydogdu
Keyword(s):  
Carbon Nanotubes ◽  
Forced Vibration ◽  
Beam Theory ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Resonance Frequencies ◽  
Non Local ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Walled Cnts

This article studies the forced vibration of the carbon nanotubes (CNTs) using the local and the non-local Euler—Bernoulli beam theory. Amplitude ratios for the local and the non-local Euler—Bernoulli beam models are given for single- and double-walled CNTs. It is found that the non-local models give higher amplitudes when compared with the local Euler—Bernoulli beam models. The non-local Euler—Bernoulli beam model predicts lower resonance frequencies.

Nonlinear Dynamic Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

2011 ◽  
Vol 2 (4) ◽  
Author(s):  
Anand Y. Joshi ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Dynamic Response ◽  
Beam Theory ◽  
Central Plane ◽  
Mass Sensor ◽  
Poincaré Maps ◽  
Single Walled Carbon Nanotube ◽  
Poincare Maps ◽  
Single Walled Carbon

In previous studies, experimentally measured resonance frequencies of carbon nanotubes have been used along with classical beam theory for straight beams. However, it is found that these carbon nanotubes are not straight, and that they have some significant surface deviation associated with them. This paper deals with the nonlinear vibration analysis of a wavy single-walled carbon nanotube based mass sensor, which is doubly clamped at a source and a drain. Nonlinear oscillations of a single-walled carbon nanotube excited harmonically near its primary resonance are considered. The carbon nanotube is excited by the addition of an excitation force. The modeling is carried out using the elastic continuum beam theory concept, which involves stretching of the central plane and phenomenological damping. This model takes into account the existence of waviness in carbon nanotubes. The equation of motion involves two nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the carbon nanotube based mass sensor is analyzed in the context of the time response, Poincaré maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. Period doubling and mechanism of intermittency have been observed as the routes to chaos. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass and the geometric imperfections of carbon nanotube. Poincaré maps and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

scholarly journals Forced Vibration Analysis of Composite Beams Reinforced by Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 571
Author(s):  
Ömer Civalek ◽  
Şeref D. Akbaş ◽  
Bekir Akgöz ◽  
Shahriar Dastjerdi
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Volume Fraction ◽  
Ritz Method ◽  
Time History ◽  
Composite Beams ◽  
Reinforced Composite ◽  
Forced Vibration Analysis

This paper presents forced vibration analysis of a simply supported beam made of carbon nanotube-reinforced composite material subjected to a harmonic point load at the midpoint of beam. The composite beam is made of a polymeric matrix and reinforced the single-walled carbon nanotubes with their various distributions. In the beam kinematics, the first-order shear deformation beam theory was used. The governing equations of problem were derived by using the Lagrange procedure. In the solution of the problem, the Ritz method was used, and algebraic polynomials were employed with the trivial functions for the Ritz method. In the solution of the forced vibration problem, the Newmark average acceleration method was applied in the time history. In the numerical examples, the effects of carbon nanotube volume fraction, aspect ratio, and dynamic parameters on the forced vibration response of carbon nanotube-reinforced composite beams are investigated. In addition, some comparison studies were performed, with special results of published papers to validate the using formulations.

Dynamic Buckling of Thermo-Electro-Mechanically Loaded FG-CNTRC Beams

2015 ◽  
Vol 15 (08) ◽  
pp. 1540017 ◽  
Author(s):  
Jie Yang ◽  
Liao-Liang Ke ◽  
Chuang Feng
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Applied Voltage ◽  
Volume Fraction ◽  
Beam Theory ◽  
Distribution Patterns ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Periodic Force ◽  
The Matrix

Functionally graded carbon nanotube reinforced nanocomposites have drawn great attention in both research and engineering communities. The weak interfacial bonding between carbon nanotubes and the matrix, which traditionally hinders the application of carbon nanotube reinforced nanocomposites, can be remarkably improved through the graded distribution of carbon nanotubes in the matrix. Within the framework of classical beam theory, this paper investigates the dynamic buckling behavior of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes and integrated with two surface bonded piezoelectric layers. The governing equations of the beam subjected to an applied voltage, a uniform temperature and an axial periodic force are derived by applying Hamilton's principle. Numerical results are presented for beams with different distribution patterns and volume fractions of carbon nanotubes and end support conditions. The influences of the beam geometry, temperature change, applied voltage, static axial force component, boundary condition, carbon nanotube volume fraction and its distribution on the unstable regions of FG-CNTRC piezoelectric beams are discussed in detail.

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