scholarly journals Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Tiantian Xu ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotubes ◽  
Electrostatic Force ◽  
Dynamic Responses ◽  
Cylindrical Shape ◽  
Beam Model ◽  
Electrostatic Forces ◽  
Complicated Form ◽  
The Galerkin Method ◽  
Integrity Analysis

Because of the inherent nonlinearities involving the behavior of carbon nanotubes (CNTs) when excited by electrostatic forces, modeling and simulating their behavior are challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This work presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of CNTs when actuated by large electrostatic forces. We study by expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler–Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

scholarly journals Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

2015 ◽  
Author(s):  
Tiantian Xu ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotubes ◽  
Electrostatic Force ◽  
Small Diameter ◽  
Dynamic Responses ◽  
Cylindrical Shape ◽  
Beam Model ◽  
Electrostatic Forces ◽  
Complicated Form ◽  
The Impact

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effect of DC voltage load and AC voltage load on the nonlinearity has been studied. We also investigated the impact of initial slack level on the natural frequency and the nonlinearity. Small diameter and large initial slacked CNTs has been considered.

scholarly journals An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

2014 ◽  
Author(s):  
Tiantian Xu ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotubes ◽  
Galerkin Method ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Complicated Form ◽  
The Galerkin Method ◽  
Expanded Form

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

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.

Pull-In Dynamics of an Elastic Beam Actuated by Distributed Electrostatic Force

2003 ◽  
Author(s):  
Slava Krylov ◽  
Ronen Maimon
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Instability ◽  
Electrostatic Force ◽  
Normal Modes ◽  
Elastic Beam ◽  
Nonlinear Damping ◽  
Rotational Inertia ◽  
Electrostatic Forces ◽  
Spatial Region ◽  
Electrically Actuated

A detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented. A model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear distributed squeezed film damping forces, and rotational inertia of a mass carried by the beam. Special attention is paid to the dynamics of the beam near instability points. Results generated by the model and confirmed experimentally show that nonlinear damping leads to shrinkage of the spatial region where stable motion is realizable. The voltage that causes dynamic instability, in turn, approaches the static pull-in value.

Nonlinear Dynamics of Simple-Supported Beam under Concentrated Moving Load

2012 ◽  
Vol 226-228 ◽  
pp. 541-545 ◽  
Author(s):  
Dong Xing Cao ◽  
Bao Chen ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Double Layer ◽  
Vibration Suppression ◽  
Structural Parameters ◽  
Moving Load ◽  
Equations Of Motion ◽  
Single Layer ◽  
Dynamic Responses ◽  
Beam Model ◽  
Layer Model

The dynamic responses of two kinds of simple-supported beams with single layer and double-layer under a moving load were analyzed based on the theory of nonlinear dynamics. The equations of motion are derived by using Hamilton’s principle and von Karman type equations for the two models. Galerkin’s method was employed to obtain the ordinary differential equations of motion. First we obtain the periodic motion waveforms in the mid-point of the beams at the same initial velocity, and the result show that the amplitude of the double-layer model is much smaller then that of the single-layer model. Then for the two models, the vibration response and critical velocity were studied considering the effect of the structural parameters, the magnitude and velocity of moving load. The results of numerical simulation show that double-layer beam model has better vibration suppression performance than single-layer beam model.

Pull-in Dynamics of an Elastic Beam Actuated by Continuously Distributed Electrostatic Force

2004 ◽  
Vol 126 (3) ◽  
pp. 332-342 ◽  
Author(s):  
Slava Krylov ◽  
Ronen Maimon
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Instability ◽  
Electrostatic Force ◽  
Normal Modes ◽  
Elastic Beam ◽  
Nonlinear Damping ◽  
Rotational Inertia ◽  
Electrostatic Forces ◽  
Spatial Region ◽  
Electrically Actuated

A detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented. A model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear squeezed film damping, and rotational inertia of a mass carried by the beam. Special attention is paid to the dynamics of the beam near instability points. Results generated by the model and confirmed experimentally show that nonlinear damping leads to shrinkage of the spatial region where stable motion is realizable. The voltage that causes dynamic instability, in turn, approaches the static pull-in value.

scholarly journals Control of Bouncing in MEMS Switches Using Double Electrodes

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Farhan Abdul Rahim ◽  
Mohammad I. Younis
Keyword(s):  
Microelectromechanical Systems ◽  
Rf Mems ◽  
Electrostatic Force ◽  
Squeeze Film ◽  
Beam Model ◽  
Mems Switches ◽  
Lumped Parameter ◽  
Rf Mems Switches ◽  
Double Electrode ◽  
The Galerkin Method

This paper presents a novel way of controlling the bouncing phenomenon commonly present in the Radio Frequency Microelectromechanical Systems (RF MEMS) switches using a double-electrode configuration. The paper discusses modeling bouncing using both lumped parameter and beam models. The simulations of bouncing and its control are discussed. Comparison between the new proposed method and other available control techniques is also made. The Galerkin method is applied on the beam model accounting for the nonlinear electrostatic force, squeeze film damping, and surface contact effect. The results indicate that it is possible to reduce bouncing and hence beam degradation, by the use of double electrodes.

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

Effects of the Gear Tooth Modification on the Nonlinear Dynamics of Gear Transmission System

2010 ◽  
Vol 97-101 ◽  
pp. 2764-2769
Author(s):  
Si Yu Chen ◽  
Jin Yuan Tang ◽  
C.W. Luo
Keyword(s):  
Nonlinear Dynamics ◽  
Gear Tooth ◽  
Simulation Method ◽  
Transmission Error ◽  
Dynamic Responses ◽  
Meshing Stiffness ◽  
Gear Transmission System ◽  
Tooth Modification ◽  
Static Transmission Error ◽  
Misalignment Error

The effects of tooth modification on the nonlinear dynamic behaviors are studied in this paper. Firstly, the static transmission error under load combined with misalignment error and modification are deduced. These effects can be introduced directly in the meshing stiffness and static transmission error models. Then the effect of two different type of tooth modification combined with misalignment error on the dynamic responses are investigated by using numerical simulation method. The numerical results show that the misalignment error has a significant effect on the static transmission error. The tooth crowning modification is generally preferred for absorbing the misalignment error by comparing with the tip and root relief. The tip and root relief can not resolve the vibration problem induced by misalignment error but the crowning modification can reduce the vibration significantly.

Nonlinear Dynamics Behavior of Tethered Submerged Buoy under Wave Loadings

2020 ◽  
Vol 21 (1) ◽  
pp. 11-21
Author(s):  
Lin Zhao ◽  
Weihao Meng ◽  
Zhongqiang Zheng ◽  
Zongyu Chang
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Behavior ◽  
Coupling Factor ◽  
Dynamic Responses ◽  
Mooring Line ◽  
Second Law ◽  
Largest Lyapunov Exponent ◽  
Nonlinear Characteristic ◽  
Runge Kutta Method ◽  
Marine Engineering

AbstractTethered submerged buoy is used extensively in the field of marine engineering. In this paper considering the effect of wave, the nonlinear dynamics behavior of tethered submerged buoy is debated under wave loadings. According to Newton’s second law, the dynamic of the system is built. The coupling factor of the system is neglected, the natural frequency is calculated. The dynamic responses of the system are analyzed using Runge–Kutta method. Considering the variety of the steepness kA, the phenomenon of dynamic behavior can be periodic, double periodic and quasi-periodic and so on. The bifurcation diagram and the largest Lyapunov exponent are applied to judge the nonlinear characteristic. It is helpful to understand the dynamic behavior of tethered submerged buoy and design the mooring line of tethered submerge buoy.

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