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 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 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.

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.

scholarly journals Analysis of Vibration Frequency of Carbon Nanotubes used as Nano-Force Sensors Considering Clamped Boundary Condition

Electronics ◽  
2019 ◽  
Vol 8 (10) ◽  
pp. 1082 ◽  
Author(s):  
Toshiaki Natsuki ◽  
Kairi Urakami
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Medium ◽  
Vibration Frequency ◽  
Small Diameter ◽  
Axial Direction ◽  
Force Sensor ◽  
Beam Model ◽  
Atomic Force ◽  
Buckling Stability ◽  
Euler Bernoulli Beam

Carbon nanotubes (CNTs) can be used as atomic force microscope (AFM) probes since they are ideal tip materials with a small diameter, high aspect ratio, and stiffness. In this study, a model of CNTs clamped in an elastic medium is proposed as nanoscale force sensing AFM probes. The relationship between vibration frequency and axial force of the CNT probe clamped in an elastic medium is analyzed based on the Euler-Bernoulli beam model and the Whitney-Riley model. The clamped length of CNTs, and the elastic modulus of elastic medium affect largely on the vibration and the buckling stability of a CNT AFM probe. The result showed that the sensitivity to vibration increases as the applied loads increase. The critical load in which the vibration frequency decreases rapidly, moving to large ones with decreasing ratio of length to diameter of CNTs. The theoretical investigation on the vibration frequency of CNT loaded in the axial direction would give a useful reference for designing a CNT used as a nano-force sensor.

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 Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

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.

scholarly journals Effect of SWCNT-Tuball Paper on the Lightning Strike Protection of CFRPs and Their Selected Mechanical Properties

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3140
Author(s):  
Kamil Dydek ◽  
Anna Boczkowska ◽  
Rafał Kozera ◽  
Paweł Durałek ◽  
Łukasz Sarniak ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Electrical Conductivity ◽  
Copper Foil ◽  
Impact Resistance ◽  
Mechanical Analysis ◽  
Lightning Strike ◽  
Single Wall Carbon Nanotubes ◽  
Carbon Fibre Reinforced Polymer ◽  
The Impact

The main aim of this work was the investigation of the possibility of replacing the heavy metallic meshes applied onto the composite structure in airplanes for lightning strike protection with a thin film of Tuball single-wall carbon nanotubes in the form of ultra-light, conductive paper. The Tuball paper studied contained 75 wt% or 90 wt% of carbon nanotubes and was applied on the top of carbon fibre reinforced polymer before fabrication of flat panels. First, the electrical conductivity, impact resistance and thermo-mechanical properties of modified laminates were measured and compared with the reference values. Then, flat panels with selected Tuball paper, expanded copper foil and reference panels were fabricated for lightning strike tests. The effectiveness of lightning strike protection was evaluated by using the ultrasonic phased-array technique. It was found that the introduction of Tuball paper on the laminates surface improved both the surface and the volume electrical conductivity by 8800% and 300%, respectively. The impact resistance was tested in two directions, perpendicular and parallel to the carbon fibres, and the values increased by 9.8% and 44%, respectively. The dynamic thermo-mechanical analysis showed higher stiffness and a slight increase in glass transition temperature of the modified laminates. Ultrasonic investigation after lightning strike tests showed that the effectiveness of Tuball paper is comparable to expanded copper foil.

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.

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