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.

Forced vibration analysis of blade after selective laser shock processing based on Timoshenko’s beam theory

2020 ◽  
Vol 243 ◽  
pp. 112249 ◽  
Author(s):  
Peilin Fu ◽  
Jianghong Yuan ◽  
Xu Zhang ◽  
Guozheng Kang ◽  
Ping Wang ◽  
...  
Keyword(s):  
Forced Vibration ◽  
Vibration Analysis ◽  
Beam Theory ◽  
Laser Shock ◽  
Laser Shock Processing ◽  
Forced Vibration Analysis ◽  
Shock Processing

Large Amplitude Forced Vibration Analysis of Stiffened Plates under Harmonic Excitation

2012 ◽  
pp. 26-61
Author(s):  
Anirban Mitra ◽  
Prasanta Sahoo ◽  
Kashinath Saha
Keyword(s):  
Free Vibration ◽  
Forced Vibration ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Mathematical Formulation ◽  
Free Vibration Analysis ◽  
Harmonic Excitation ◽  
Stiffened Plates ◽  
Backbone Curve ◽  
Forced Vibration Analysis

Large amplitude forced vibration behaviour of stiffened plates under harmonic excitation is studied numerically incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Large amplitude free vibration analysis of the same system is carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the set of governing equations for both forced and free vibration problems derived using Hamilton’s principle. Appropriate sets of coordinate functions are formed by following the two dimensional Gram-Schmidt orthogonalization procedure to satisfy the corresponding boundary conditions of the plate. The problem is solved by employing an iterative direct substitution method with an appropriate relaxation technique and when the system becomes computationally stiff, Broyden’s method is used. The results are furnished as frequency response curves along with the backbone curve in the dimensionless amplitude-frequency plane. Three dimensional operational deflection shape (ODS) plots and contour plots are provided in a few cases.

Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity

2015 ◽  
Vol 3 (4) ◽  
pp. 193-206 ◽  
Author(s):  
Awda Chemi ◽  
Houari Heireche ◽  
Mohamed Zidour ◽  
Kaddour Rakrak ◽  
Abdelmoumen Anis Bousahla
Keyword(s):  
Carbon Nanotube ◽  
Buckling Load ◽  
Local Theory ◽  
Critical Buckling Load ◽  
Non Local

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.

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.

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 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.

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