Application of Nonlinear Systems in Nanomechanics and Nanofluids (eBook)

Analytical Methods and Applications

Davood Domairry Ganji, Sayyid Habibollah Hashemi Kachapi (Autoren)

eBook Download: PDF | EPUB

2015 | 1. Auflage
412 Seiten
Elsevier Science (Verlag)
978-0-323-35381-6 (ISBN)

Infos

With Application of Nonlinear Systems in Nanomechanics and Nanofluids the reader gains a deep and practice-oriented understanding of nonlinear systems within areas of nanotechnology application as well as the necessary knowledge enabling the handling of such systems. The book helps readers understand relevant methods and techniques for solving nonlinear problems, and is an invaluable reference for researchers, professionals and PhD students interested in research areas and industries where nanofluidics and dynamic nano-mechanical systems are studied or applied. The book is useful in areas such as nanoelectronics and bionanotechnology, and the underlying framework can also be applied to other problems in various fields of engineering and applied sciences. - Provides comprehensive coverage of nano-dynamical systems and their specialized processes and applications in the context of nonlinear differential equations and analytical methods - Enables researchers and engineers to better model, interpret and control nanofluidics and other nano-dynamical systems and their application processes - Explains nano-dynamical systems by means of describing 'real-life' application case studies

D. D. Ganji is a Professor of Mechanical Engineering and the Director of the Graduate Program at Babol Noshirvani University of Technology in Iran, as well as a consultant in nonlinear dynamics and the Dean of the National Elite Foundation of Iran. He has a Ph.D. in Mechanical Engineering from Tarbiat Modarres University. He is the Editor-in-Chief of International Journal of Nonlinear Dynamic and Engineering Science, and Editor of International Journal of Nonlinear Sciences and Numerical Simulation and International Journal of Differential Equations.

Textauszug

Chapter 2

Semi Nonlinear Analysis in Carbon Nanotube

Abstract

In this chapter, at first, we have presented an introduction to carbon nanotubes (CNTs). Then, the more important applications of CNTs are introduced in separate sections and nonlinear dynamical systems arose from those have been solved by semi important and strongly analytical and numerical methods. In each section, we have discussed the affecting important parameters on the physics of the problems.

In the first section of this chapter, the deformation of an individual single-walled carbon nanotube (SWCNT) over a bundle of nanotubes has been studied using the generalized differential quadrature method. In the second section, the continuum mechanics method and a bending model are applied to obtain the resonant frequency of the fixed-free SWCNT where the mass is rigidly attached to the tip. The validity and the accuracy of these formulas are examined with other sensor equations in the literatures. In the third section, based on continuum mechanics and an elastic beam model, a nonlinear free vibration analysis of embedded SWCNT considering the effects of rippling deformation and midplane stretching on nonlinear frequency is investigated and more, in fourth section, continuum mechanics and an elastic beam model have been introduced in the nonlinear force vibrational analysis of an embedded, curved, SWCNT and finally, in fifth section, based on the rippling deformation, a nonlinear beam model is developed for transverse vibration of SWCNTs on elastic foundation. The nonlinear natural frequency has been calculated for typical boundary conditions using the perturbation method of multiscales.

Keywords

Nanotube

Carbon nanotube

Tubular carbon structures

Curved carbon nanotube

Single-walled carbon nanotube

Nanobeam

Nonlinear dynamic

Nonlinear vibration

Generalized differential quadrature method

Continuum mechanics method

Variational iteration method

Energy balance method

Galerkin method

Runge-Kutta method

Euler-Bernoulli theory

Resonant frequency

Cantilevered boundary conditions

Sensor equations

Midplane stretching

Elastic foundation

Pasternak foundation

Winkler foundation

Nonlinear bending deformation

Rippling deformation

Chapter Contents

2.1 Introduction of Carbon Nanotube   14

2.1.1 Single-Wall Nanotubes   15

2.1.2 Multiwall Nanotubes   15

2.1.3 Double-Wall Nanotubes   15

2.2 Single SWCNT Over a Bundle of Nanotube   17

2.2.1 Introduction   17

2.2.2 Formulations   18

2.2.2.1 Schematic of Problem   18

2.2.2.2 Modeling the Individual SWCNT as a Beam   19

2.2.2.3 Differential Quadrature and Solution Procedure   20

2.2.2.4 Finite Element Method   22

2.2.3 Results   24

2.2.3.1 Mesh Point Number Effect   24

2.2.3.2 Length Effect   25

2.2.3.3 Validation of GDQ Approach   25

2.2.4 Conclusion   27

2.3 Cantilevered SWCNT as a Nanomechanical Sensor   28

2.3.1 Introduction   30

2.3.2 Analysis of the Problem   31

2.3.2.1 Basic Bending Vibration and Resonant Frequencies of SWCNT with Attached Mass   31

2.3.2.2 Resonant Frequency of Cantilevered SWCNT Where the Mass is Rigidly Attached to the Tip   31

2.3.3 Numerical Results   33

2.3.3.1 Vibration Mode Analysis   33

2.3.4 Mass Sensor Mode Comparison   33

2.3.5 Conclusion   35

2.4 Nonlinear Vibration for Embedded CNT   36

2.4.1 Introduction   36

2.4.2 Basic Equations   37

2.4.3 Solution Methodology   40

2.4.4 Numerical Results and Discussion   41

2.4.5 Conclusion   45

2.5 Curved SWCNT   45

2.5.1 Introduction   45

2.5.2 Vibrational Model   46

2.5.3 Solution Methodology   48

2.5.4 Numerical Results and Discussion   49

2.5.5 Conclusion   53

2.6 CNT with Rippling Deformations   54

2.6.1 Introduction   54

2.6.2 Vibration Model   55

2.6.2.1 Boundary Conditions   55

2.6.2.2 Nonlinear Vibration Model   55

2.6.2.3 Nonlinear Analysis   57

2.6.3 Results and Discussion   62

2.6.4 Conclusion   67

References   68

2.1 Introduction of Carbon Nanotube

Since their initial discovery by Iijima (1991), carbon nanotubes (CNTs) have come under ever-increasing scientific scrutiny.

A CNT is a tube-shaped material, made of carbon, having a diameter measuring on the nanometer scale. A nanometer is one-billionth of a meter, or about one ten-thousandth of the thickness of a human hair. The graphite layer appears somewhat like a rolled-up chicken wire with a continuous unbroken hexagonal mesh and carbon molecules at the apexes of the hexagons.

CNTs have many structures, differing in length, thickness, and in the type of helicity and number of layers. CNTs possess excellent mechanical properties, such as extremely high strength, stiffness, and resilience. These points, together with other distinctive physical properties, result in many prospective applications, such as strong, light, and high toughness fibers for nanocomposite structures, parts of nanodevices, hydrogen storage (high frequency) micromechanical oscillators, etc. (see www.nanocyl.com/en/CNT-Expertise-Centre/Carbon-Nanotubes).

In fact, CNTs are unique nanostructured materials. The extraordinary mechanical and physical properties in addition to the large aspect ratio and low density have made CNTs ideal components of nanodevices.

Although they are formed from essentially the same graphite sheet, their electrical characteristics differ depending on these variations, acting either as metals or as semiconductors.

As a group, CNTs typically have diameters ranging from < 1 up to 50 nm. Their lengths are typically several microns, but recent advancements have made the nanotubes much longer, and measured in centimeters.

CNTs can be categorized by their structures:

1. Single-wall nanotubes (SWNT)

2. Multiwall nanotubes (MWNT)

3. Double-wall nanotubes (DWNT)

2.1.1 Single-Wall Nanotubes

SWNT are tubes of graphite that are normally capped at the ends. They have a single cylindrical wall. The structure of a SWNT can be visualized as a layer of graphite, a single atom thick, called graphene, which is rolled into a seamless cylinder.

Most SWNT typically have a diameter of close to 1 nm. The tube length, however, can be many thousands of times longer.

SWNT are more pliable yet harder to make than MWNT. They can be twisted, flattened, and bent into small circles or around sharp bends without breaking.

SWNT have unique electronic and mechanical properties which can be used in numerous applications, such as field-emission displays, nanocomposite materials,...

Produkt-Details

• Erscheint lt. Verlag: 19.3.2015
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• ISBN-10: 0-323-35381-9 / 0323353819
• ISBN-13: 978-0-323-35381-6 / 9780323353816