Carbon nanotubes and nanosensors : vibration, buckling and ballistic impact / Isaac Elishakoff ... [and others].

Format:

Book

Contributor:

Elishakoff, Isaac.

Language:

English

Subjects (All):

Nanotubes--Impact testing.

Nanotubes.

Nanotubes--Elastic properties.

Detectors--Testing.

Detectors.

Elasticity.

Impact--Testing.

Physical Description:

xiii, 421 pages : illustrations ; 24 cm

Place of Publication:

London : ISTE ; Hoboken, NJ : Wiley, 2012.

Summary:

It may be sobering to learn that tubes measuring in the scale of nanometers, the cutting edge of materials science and engineering, can suffer that same kind of problems as the water pipes in your house. Chemists and materials scientists from many countries explore such topics as fundamental natural frequencies of double-walled carbon nanotubes, free vibrations of the triple-walled carbon nanotube, natural frequencies of carbon nanotubes based on a consistent version of Bresse-Timoshenko theory, the buckling of a double-walled carbon nanotube, some fundamental aspects of non-local beam mechanics for nanostructures applications, and surface effects of natural frequencies of double-walled carbon nanotubes. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)

Contents:

Chapter 1 Introduction 1

1.1 The need of determining the natural frequencies and buckling loads of CNTs 8

1.2 Detenrunation of natural frequencies of SWCNT as a uniform beam model and MWCNT during coaxial deflection 8

1.3 Beam model of MWCNT 9

1.4 CNTs embedded in an elastic medium 10

Chapter 2 Fundamental Natural Frequencies of Double-Walled Carbon Nanotubes 13

2.1 Background 13

2.2 Analysis 15

2.3 Simply supported DWCNT: exact solution 15

2.4 Simply supported DWCNT: Bubnov-Galerkin method 18

2.5 Simply supported DWCNT: Petrov-Galerkin method 20

2.6 Clamped-clamped DWCNT: Bubnov-Galerkin method 23

2.7 Clamped-clamped DWCNT: Petrov-Galerkin method 25

2.8 Simply supported-clamped DWCNT 27

2.9 Clamped-free DWCNT 30

2.10 Comparison with results of Natsuki et al. [NAT 08a] 33

2.11 On closing the gap on carbon nanotubes 34

2.11.1 Linear analysis 34

2.11.2 Nonlinear analysis 40

2.12 Discussion 45

Chapter 3 Free Vibrations of the Triple-Walled Carbon Nanotubes 47

3.1 Background 47

3.2 Analysis 48

3.3 Simply supported TWCNT: exact solution 49

3.4 Simply supported TWCNT: approximate solutions 51

3.5 Clamped-clamped TWCNT: approximate solutions 54

3.6 Simply supported-clamped TWCNT: approximate solutions 57

3.7 Clamped-free TWCNT: approximate solutions 60

3.8 Summary 63

Chapter 4 Exact Solution for Natural Frequencies of Clamped-Clamped Double-Walled Carbon Nanotubes 65

4.1 Background 65

4.2 Analysis 67

4.3 Analytical exact solution 72

4.4 Numerical results and discussion 77

4.4.1 Bubnov-Galerkin method 81

4.5 Discussion 82

4.6 Summary 83

Chapter 5 Natural Frequencies of Carbon Nanotubes Based on a Consistent Version of Bresse-Timoshenko Theory 85

5.1 Background 85

5.2 Bresse-Timoshenko equations for homogeneous beams 86

5.3 DWCNT modeled on the basis of consistent Bresse-Timoshenko equations 88

5.4 Numerical results and discussion 91

Chapter 6 Natural Frequencies of Double-Walled Carbon Nanotubes Based on Donnell Shell Theory 97

6.1 Background 97

6.2 Donnell shell theory for the vibration of MWCNTs 99

6.3 Donnell shell theory for the vibration of a simply supported DWCNT 100

6.4 DWCNT modeled on the basis of simplified Donnell shell theory 103

6.5 Further simplifications of the Donnell shell theory 105

6.6 Summary 107

Chapter 7 Buckling of a Double-Walled Carbon Nanotube 109

7.1 Background 109

7.2 Analysis 111

7.3 Simply supported DWCNT: exact solution 112

7.4 Simply supported DWCNT: Bubnov-Galerkin method 114

7.5 Simply supported DWCNTs: Petrov-Galerkin method 116

7.6 Clamped-clamped DWCNT 117

7.7 Simply supported-clamped DWCNT 119

7.8 Buckling of a clamped-free DWCNT by finite difference method 121

7.9 Buckling of a clamped-free DWCNT by Bubnov-Galerkin method 131

7.9.1 Analysis 131

7.9.2 Results 135

7.9.3 Conclusion 137

7.10 Summary 137

Chapter 8 Ballistic Impact on a Single-Walled Carbon Nanotube 139

8.1 Background 139

8.2 Analysis 140

8.3 Numerical results and discussion 144

Chapter 9 Clamped-Free Double-Walled Carbon Nanotube-Based Mass Sensor 149

9.1 Introduction 149

9.2 Basic equations 150

9.3 Vibration frequencies of DWCNT with light bacterium at the end of outer nanotube 152

9.4 Vibration frequencies of DWCNT with heavy bacterium at the end of outer nanotube 159

9.5 Vibration frequencies of DWCNT with light bacterium at the end of inner nanotube 165

9.6 Vibration frequencies of DWCNT with heavy bacterium at the end of inner nanotube 170

9.7 Numerical results 176

9.8 Effective stiffness and effective mass of the double-walled carbon nanotube sensor 178

9.8.1 Introduction 178

9.8.2 Bubnov-Galerkin method 179

9.8.3 Finite-difference method 182

9.8.4 Effective mass of DWCNT with bacterium at the end 186

9.8.5 Conclusions 190

9.9 Virus sensor based on single-walled carbon nanotube treated as Bresse-Timoshenko beam 190

9.9.1 Introduction 190

9.9.2 Analysis 191

9.9.3 Results 197

9.9.4 Mimivirus 200

9.10 Conclusion 201

Chapter 10 Some Fundamental Aspects of Non-local Beam Mechanics for Nanostructures Applications 203

10.1 Background on the need of non-locality 204

10.2 Non-local beam models 209

10.2.1 Beam mechanics and Eringen's non-local model 209

10.2.2 Beam mechanics and gradient elasticity model 212

10.2.3 How to connect gradient elasticity with non-local integral models? 216

10.3 The cantilever case: a structural paradigm 218

10.3.1 Introduction 218

10.3.2 Eringen's integral model 219

10.3.3 Gradient elastic beam 221

10.3.4 Non-local elastic beam based on strain energy functional with squared non-local curvature 224

10.3.5 New non-local elastic beam model based on strain energy functional with mixed local and non-local curvatures 225

10.4 Euler-Bernoulli beam: Eringen's based model 231

10.4.1 Buckling of non-local Euler-Bernoulli beams 231

10.4.2 Vibrations of non-local Euler-Bernoulli beams 233

10.5 Euler-Bernoulli beam: gradient elasticity model 234

10.5.1 Buckling of gradient elasticity Euler-Bernoulli beams 234

10.5.2 Vibrations of gradient elasticity Euler-Bernoulli beams 235

10.6 Euler-Bernoulli beam: hybrid non-local elasticity model 236

10.6.1 Buckling of hybrid non-local Euler-Bernoulli beams 236

10.6.2 Vibrations of hybrid non-local Euler-Bemoulli beams 237

10.7 Timoshenko beam: Eringen's based model 238

10.7.1 Buckling of non-local Engesser Timoshenko beams 238

10.7.2 Buckling of non-local Haringx Timoshenko beams 240

10.7.3 Vibrations of non-local Timoshenko beams 242

10.8 Timoshenko beam: gradient elasticity model 244

10.8.1 Buckling of gradient Timoshenko beam with Engesser's theory 244

10.8.2 Buckling of gradient Timoshenko beam with Haringx's theory 246

10.8.3 Vibrations of gradient Timoshenko beam 247

10.8.4 Some other Timoshenko gradient elasticity beam models 249

10.9 Timoshenko beam, hybrid non-local elasticity model 251

10.9.1 Buckling of the hybrid Engesser's non-local Timoshenko beam 251

10.9.2 Vibrations of the hybrid non-local Timoshenko beam 252

10.10 Higher order shear beam: Eringen's based model 254

10.10.1 Buckling of non-local higher order shear beam 254

10.10.2 Vibrations of non-local higher order shear beam 257

10.11 Higher order shear beam, gradient elasticity model 259

10.11.1 Buckling of gradient Engesser higher order shear beam 259

10.11.2 Vibrations of gradient higher order shear beam 260

10.12 Validity of the results for double-nanobeam systems 262

10.12.1 Buckling of non-local double-nanobeam systems 262

10.12.2 Vibrations of non-local double-nanobeam systems 265

10.12.3 Buckling of gradient double-nanobeam systems 266

10.12.4 Vibrations of gradient double-nanobeam systems 267

Chapter 11 Surface Effects on the Natural Frequencies of Double-Walled Carbon Nanotubes 269

11.1 Background 269

11.2 Analysis 271

11.2.1 Non-local Bresse-Timoshenko beam theory 272

11.2.2 Van der Waals interaction forces 274

11.2.3 Natural vibration of DWCNTs 275

11.2.4 Free vibration of embedded DWCNTs 278

11.3 Results and discussion 279

11.4 Surface effects on buckling of nanotubes 286

11.5 Summary 289

Chapter 12 Summary and Directions for Future Research 291.

Notes:

Includes bibliographical references and indexes.

ISBN:

9781848213456

184821345X

OCLC:

761481960

Online:

Publisher description