Nonlinear Vibration and Stability Analysis of Embedded Carbon Nanotubes With Internal Flow

2010 ◽  
Author(s):  
M. Rasekh ◽  
S. E. Khadem
Keyword(s):  
Carbon Nanotube ◽  
Nonlinear Vibration ◽  
Elastic Medium ◽  
Multiple Scales ◽  
Internal Flow ◽  
Beam Theory ◽  
Response Curves ◽  
Critical Flow Velocity ◽  
Aspect Ratios ◽  
The Stability

In this paper, for the first time, the influence of internal moving fluid on the nonlinear vibration and stability of embedded carbon nanotube is investigated. The Euler-Bernoulli beam theory is employed to model the vibrational behavior of an embedded carbon nanotube. The relationship of nonlinear amplitude and frequency for the single-wall nanotubes in the presence of internal fluid flow is expressed using the multiple scales perturbation method. The amplitude-frequency response curves of the nonlinear vibration obtained and the effects of the surrounding elastic medium, mass and the aspect ratios of nanotubes are discussed. It is shown that beyond the critical flow velocity buckling occurs and surrounding elastic medium plays a significant role in the stability of the carbon nanotube.

An efficient GDQ model for vibration analysis of a multiwall carbon nanotube on Pasternak foundation with general boundary conditions

2011 ◽  
Vol 225 (7) ◽  
pp. 1730-1741 ◽  
Author(s):  
P Soltani ◽  
P Bahar ◽  
A Farshidianfar
Keyword(s):  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Elastic Medium ◽  
Differential Quadrature Method ◽  
Elastic Beam ◽  
Beam Theory ◽  
Multiwall Carbon Nanotube ◽  
Various Boundary Conditions ◽  
Aspect Ratios ◽  
Multiwall Carbon

In this article, the free transverse vibrational behaviour of a multiwall carbon nanotube (MWNT) surrounded by a Pasternak-type elastic medium has been determined using a very generalized model. The model has been made on the basis of Timoshenko elastic beam theory which allows the effects of shear deformation and rotary inertia and supports non-coaxial vibration of the adjacent layers of MWNT using interlayer van der Waals forces. The boundary conditions used in this simulation are such that not only standard and conventional kinds, but also all possible forms, of end conditions are applicable. A generalized differential quadrature method is utilized to solve the governing equations with assorted aspect ratios, various boundary conditions, and different foundation stiffnesses. This study shows that the resonant frequencies of MWNTs are strongly dependent on the stiffness of the elastic medium, aspect ratios, and number of walls in carbon nanotubes and, for short nanotubes, the boundary stiffness plays a significant role on the natural frequencies.

scholarly journals Study on the nonlinear vibration of embedded carbon nanotube via the Hamiltonian-based method

2021 ◽  
pp. 146134842110327
Author(s):  
Kang-Jia Wang ◽  
Guo-Dong Wang
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Nonlinear Vibration ◽  
Elastic Medium ◽  
Numerical Results ◽  
Frequency Property ◽  
New Novel ◽  
Novel Method

This article mainly studies the vibration of the carbon nanotubes embedded in elastic medium. A new novel method called the Hamiltonian-based method is applied to determine the frequency property of the nonlinear vibration. Finally, the effectiveness and reliability of the proposed method is verified through the numerical results. The obtained results in this work are expected to be helpful for the study of the nonlinear vibration.

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.

Analysis of Transverse Vibration of Axially Moving Viscoelastic Sandwich Beam with Time-Dependent Velocity

2011 ◽  
Vol 338 ◽  
pp. 487-490 ◽  
Author(s):  
Hai Wei Lv ◽  
Ying Hui Li ◽  
Qi Kuan Liu ◽  
Liang Li
Keyword(s):  
Transverse Vibration ◽  
Multiple Scales ◽  
Sandwich Beam ◽  
Core Layer ◽  
Response Elimination ◽  
Response Curves ◽  
Mean Velocity ◽  
State Response ◽  
Axially Moving ◽  
The Stability

Transverse vibration of an axially moving viscoelastic sandwich beam is investigated in this paper. Based on the Kelvin constitutive equation, transverse controlling equation is established. First of all, the multiple scales method is applied to obtained steady-state response. Elimination of scales terms will give us the amplitude of vibrations. Additionally, the stability conditions of trivial and non-trivial solutions are analyzed using Routh-Hurwitz criterion. Eventually, numerical results are obtained to show the thickness of core layer, mean velocity, the amplitude of fluctuation effects on natural frequencies and response curves.

scholarly journals Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances

1998 ◽  
Vol 5 (5-6) ◽  
pp. 277-288 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Haider N. Arafat
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Nonlinear Ordinary Differential Equations ◽  
Response Curves ◽  
First Order ◽  
Aspect Ratios

The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.

Frequency Response of Parametric Resonance of Double Wall Carbon Nanotube Under Electrostatic Actuation for Noncoaxial Vibration

2017 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotube ◽  
Frequency Response ◽  
Multiple Scales ◽  
Van Der Waals ◽  
First Order ◽  
Electrostatically Actuated ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
Steady State Solutions ◽  
High Length

In this paper, the Method of Multiple Scales is used to investigate the influences of dimensionless damping and voltage parameters on the amplitude-frequency response of an electrostatically actuated double-walled carbon nanotube. The forces responsible for the nonlinearities in the vibrational behavior are intertube van der Waals and electrostatic forces. Soft AC excitation and small viscous damping forces are assumed. Herein, the noncoaxial case is investigated at near-zero amplitude conditions in the free vibration, which eliminates the influence of the cubic van der Waals in the first-order solution. The DWCNT structure is modelled as a cantilever beam with Euler-Bernoulli beam assumptions since the DWCNT is characterized with high length-diameter ratio. The results shown assume steady-state solutions in the first-order MMS solution. The importance of the results in this paper are the effect of damping and detuning frequency on the stability of the DWCNT vibration.

scholarly journals Temperature Effects on Nonlinear Vibration Behaviors of Euler-Bernoulli Beams with Different Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yaobing Zhao ◽  
Chaohui Huang
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Temperature Effects ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
Response Curves ◽  
Different Boundary Conditions ◽  
The Stability ◽  
The Galerkin Method ◽  
Close Form

This paper is concerned with temperature effects on the modeling and vibration characteristics of Euler-Bernoulli beams with symmetric and nonsymmetric boundary conditions. It is assumed that in the considered model the temperature increases/decreases instantly, and the temperature variation is uniformly distributed along the length and the cross-section. By using the extended Hamilton’s principle, the mathematical model which takes into account thermal and mechanical loadings, represented by partial differential equations (PDEs), is established. The PDEs of the planar motion are discretized to a set of second-order ordinary differential equations by using the Galerkin method. As to three different boundary conditions, eigenvalue analyses are performed to obtain the close-form eigenvalue solutions. First four natural frequencies with thermal effects are investigated. By using the Lindstedt-Poincaré method and multiple scales method, the approximate solutions of the nonlinear free and forced vibrations (primary, super, and subharmonic resonances) are obtained. The influences of temperature variations on response amplitudes, the localisation of the resonance zones, and the stability of the steady-state solutions are investigated, through examining frequency response curves and excitation response curves. Numerical results show that response amplitudes, the number and the stability of nontrivial solutions, and the hardening-spring characteristics are all closely related to temperature changes. As to temperature effects on vibration behaviors of structures, different boundary conditions should be paid more attention.

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