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.

Nonlinear Dynamics of Electrically-Actuated Carbon Nanotube Resonator

2008 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotube ◽  
Natural Frequency ◽  
Primary Resonance ◽  
Beam Model ◽  
Harmonic Load ◽  
Shooting Technique ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

This paper presents an investigation into the nonlinear dynamics of a carbon nanotube (CNT) actuated electrically by a DC force and an AC harmonic load. The CNT is described by an Euler Bernoulli beam model that accounts for the system nonlinearities due to mid-plane stretching and electrostatic forcing. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic response of the CNT. The static deflection of the CNT and its pull-in voltage are calculated and validated by comparing them to published results. It was found that mid-plane stretching has a major impact on the pull-in prediction of CNT. Dynamic analysis is conducted to explore the nonlinear oscillation of the CNT near its fundamental natural frequency (primary resonance) and near one half, twice, and three times its natural frequency (secondary resonances). The nonlinear analysis is carried out using a shooting technique combined with the Floquet theory to capture periodic orbits and analyze their stability. The results show that these resonances can lead to complex nonlinear dynamics phenomena such as hysteresis, dynamic pull-in, hardening and softening behaviors, and frequencies bands with an inevitable escape from a potential well.

Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite resting on viscoelastic foundation

2019 ◽  
Vol 55 (1-2) ◽  
pp. 53-68
Author(s):  
Farzad Ebrahimi ◽  
S Hamed S Hosseini
Keyword(s):  
Forced Vibration ◽  
Functionally Graded ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Electric Voltage ◽  
Modulation Equation ◽  
Flexoelectric Effect ◽  
Nonlinear Forced Vibration ◽  
Piezoelectric Structures ◽  
Porous Nanocomposite

Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite is the objective of this study. The nanocomposite is exposed to electric voltage and external parametric excitation. First, a functionally graded porous core nanoplate is modeled and then two piezoelectric layers are glued with core. It is also rested on a visco-Pasternak foundation. Second, to derive governing equation of motion, two theories including Mindlin and Kirchhoff plate theories and Hamilton’s principle are utilized. In the next step, to obtain and solve ordinary differential equation, Galerkin technique and multiple time scales method are used, respectively. At the end, modulation equation of piezoelectric/functionally graded porous nanocomposite for both primary and secondary resonances is obtained and discussed. Emphasizing the effect of piezoelectric and flexoelectric, von Karman nonlinear deformation and parametric external excitation are simultaneously taken into account. It is found that electric voltage has no effect on the performance of piezoelectricity and flexoelectricity of the material on vibration behavior. The results of this study can be useful as benchmark for the next investigations in field of energy harvesting systems and piezoelectric structures.

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.

Flow-Induced Nonlinear Vibration of Non-Uniform Nanotubes

2017 ◽  
Author(s):  
Shamim Mashrouteh ◽  
Ahmad Barari ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Nonlinear Vibration ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Beam Theory ◽  
Harmonic Excitation ◽  
Free Form ◽  
B Splines ◽  
Nonlinear Forced Vibration ◽  
Forced Vibration Analysis ◽  
Euler Bernoulli Beam

This paper focuses on nonlinear forced vibration analysis of a free-form conveying fluid nanotube. Non-Uniform Rational B-Splines (NURBS) is used to model the free-form curvature of the nanotube, analytically. In order to develop the ordinary differential equations of motion, the Euler-Bernoulli beam theory and Galerkin method are implemented and the frequency response and the primary resonance of the nanotube under a harmonic excitation are studied. The effects of the free-form curvature of the nanotube and its physical characteristic on the nonlinear vibration behavior of the system are discussed as a parametric study.

Nonlinear Forced Vibration of a Beam-Type Resonator With Attached Eccentric Mass

2014 ◽  
Author(s):  
Pezhman A. Hassanpour
Keyword(s):  
Forced Vibration ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Nonlinear Resonance ◽  
Beam Theory ◽  
Attached Mass ◽  
Beam Type ◽  
Nonlinear Forced Vibration ◽  
Euler Bernoulli Beam

In this paper, the nonlinear model of an asymmetric micro-bridge resonator with an attached eccentric mass is investigated. The resonator is treated using the Euler-Bernoulli beam theory. The attached mass represents the electrostatic comb-drive actuator in micro-electromechanical applications. The center of mass of the actuator is assumed to be off the neutral axis of the beam. The governing equations of motion are derived assuming that a concentrated harmonic force is applied to the attached mass. The nonlinear forced vibration of the system is studied using the method of multiple scales. It has been demonstrated that the eccentricity of the mass may lead to different types of nonlinear resonance, e.g., superharmonic and internal resonance. The end application of the structure under investigation is in resonant sensing and energy harvesting applications.

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yan-Shin Shih ◽  
Chen-Yuan Chung
Keyword(s):  
Governing Equation ◽  
Moving Boundary ◽  
Beam Theory ◽  
Crack Model ◽  
Breathing Crack ◽  
Connecting Rod ◽  
Bernoulli Beam ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Crank Mechanism

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

Nonlinear Forced Vibration Analysis of Smart Curved CNTs Conveying Fluid

2021 ◽  
Author(s):  
Vahid Mohamadhashemi ◽  
Amir Jalali ◽  
Habib Ahmadi
Keyword(s):  
Carbon Nanotube ◽  
Velocity Vector ◽  
Multiple Scales ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Maximum Amplitude ◽  
Beam Theory ◽  
Physical Parameters ◽  
Conveying Fluid

In this study, the nonlinear vibration of a curved carbon nanotube conveying fluid is analyzed. The nanotube is assumed to be covered by a piezoelectric layer and the Euler–Bernoulli beam theory is employed to establish the governing equations of motion. The influence of carbon nanotube curvature on structural modeling and fluid velocity vector is considered and the slip boundary conditions of CNT conveying fluid are included. The mathematical modeling of the structure is developed using Hamilton’s principle and then, the Galerkin procedure is employed to discretize the equation of motion. Furthermore, the frequency response of the system is extracted by applying the multiple scales method of perturbation. Finally, a comprehensive study is carried out on the primary resonance and piezoelectric-based parametric resonance of the system. It is shown that consideration of nanotube curvature may lead to an increase in nonlinearity. Implementing the fluid velocity vector in which nanotube curvature is included highly affects the maximum amplitude of the response and should not be ignored. Furthermore, different system parameters have evident impacts on the behavior of the system and therefore, selecting the reasonable geometrical and physical parameters of the system can be very useful to achieve a favorable response.

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