Carbon Nanotubes and Nanosensors

Prof. Isaac Elishakoff, Florida Atlantic University, USA.Dr. Demetris Pentaras, Cyprus University of Technology, Cyprus.Ing. Kevin Dujat and Ing. Simon Bucas, IFMA – French Institute for Advanced Mechanics, France.Dr. Claudia Versaci and Prof. Giuseppe Muscolino, University of Messina, Italy.Dr. Joel Storch, Touro College, USA.Prof. Noël Challamel, University of South Brittany, France.Prof. Toshiaki Natsuki, Shinsu University, Japan.Dr. Yingyan Zhang, University of Western Sydney, Australia.Prof. Chien Ming Wang, National University of Singapore, Singapore.Ing. Guillaume Ghyselinck, Ecole des Mines d’Alès, France.

• Preface xiChapter 1. Introduction 11.1. The need of determining the natural frequencies and buckling loads of CNTs 81.2. Determination of natural frequencies of SWCNT as a uniform beam model and MWCNT during coaxial deflection 81.3. Beam model of MWCNT 91.4. CNTs embedded in an elastic medium 10Chapter 2. Fundamental Natural Frequencies of Double-Walled Carbon Nanotubes 132.1. Background 132.2. Analysis 152.3. Simply supported DWCNT: exact solution 152.4. Simply supported DWCNT: Bubnov–Galerkin method 182.5. Simply supported DWCNT: Petrov–Galerkin method 202.6. Clamped-clamped DWCNT: Bubnov–Galerkin method 232.7. Clamped-clamped DWCNT: Petrov–Galerkin method 252.8. Simply supported-clamped DWCNT 272.9. Clamped-free DWCNT 302.10. Comparison with results of Natsuki et al. [NAT 08a] 332.11. On closing the gap on carbon nanotubes 342.12. Discussion 45Chapter 3. Free Vibrations of the Triple-Walled Carbon Nanotubes 473.1. Background 473.2. Analysis 483.3. Simply supported TWCNT: exact solution 493.4. Simply supported TWCNT: approximate solutions 513.5. Clamped-clamped TWCNT: approximate solutions 543.6. Simply supported-clamped TWCNT: approximate solutions 573.7. Clamped-free TWCNT: approximate solutions 603.8. Summary 63Chapter 4. Exact Solution for Natural Frequencies of Clamped-Clamped Double-Walled Carbon Nanotubes 654.1. Background 654.2. Analysis 674.3. Analytical exact solution 724.4. Numerical results and discussion 774.5. Discussion 824.6. Summary 83Chapter 5. Natural Frequencies of Carbon Nanotubes Based on a Consistent Version of Bresse–Timoshenko Theory 855.1. Background 855.2. Bresse–Timoshenko equations for homogeneous beams 865.3. DWCNT modeled on the basis of consistent Bresse–Timoshenko equations 885.4. Numerical results and discussion 91Chapter 6. Natural Frequencies of Double-Walled Carbon Nanotubes Based on Donnell Shell Theory 976.1. Background 976.2. Donnell shell theory for the vibration of MWCNTs 996.3. Donnell shell theory for the vibration of a simply supported DWCNT 1006.4. DWCNT modeled on the basis of simplified Donnell shell theory 1036.5. Further simplifications of the Donnell shell theory 1056.6. Summary 107Chapter 7. Buckling of a Double-Walled Carbon Nanotube 1097.1. Background 1097.2. Analysis 1117.3. Simply supported DWCNT: exact solution 1127.4. Simply supported DWCNT: Bubnov–Galerkin method 1147.5. Simply supported DWCNTs: Petrov–Galerkin method 1167.6. Clamped-clamped DWCNT 1177.7. Simply supported-clamped DWCNT 1197.8. Buckling of a clamped-free DWCNT by finite difference method 1217.9. Buckling of a clamped-free DWCNT by Bubnov–Galerkin method 1317.10. Summary 137Chapter 8. Ballistic Impact on a Single-Walled Carbon Nanotube 1398.1. Background 1398.2. Analysis 1408.3. Numerical results and discussion 144Chapter 9. Clamped-Free Double-Walled Carbon Nanotube-Based Mass Sensor 1499.1. Introduction 1499.2. Basic equations 1509.3. Vibration frequencies of DWCNT with light bacterium at the end of outer nanotube 1529.4. Vibration frequencies of DWCNT with heavy bacterium at the end of outer nanotube 1599.5. Vibration frequencies of DWCNT with light bacterium at the end of inner nanotube 1659.6. Vibration frequencies of DWCNT with heavy bacterium at the end of inner nanotube 1709.7. Numerical results 1769.8. Effective stiffness and effective mass of the double-walled carbon nanotube sensor 1789.9. Virus sensor based on single-walled carbon nanotube treated as Bresse–Timoshenko beam 1909.10. Conclusion 201Chapter 10. Some Fundamental Aspects of Non-local Beam Mechanics for Nanostructures Applications 20310.1. Background on the need of non-locality 20410.2. Non-local beam models 20910.3. The cantilever case: a structural paradigm 21810.4. Euler–Bernoulli beam: Eringen’s based model 23110.5. Euler–Bernoulli beam: gradient elasticity model 23410.6. Euler–Bernoulli beam: hybrid non-local elasticity model 23610.7. Timoshenko beam: Eringen’s based model 23810.8. Timoshenko beam: gradient elasticity model 24410.9. Timoshenko beam, hybrid non-local elasticity model 25110.10. Higher order shear beam: Eringen’s based model 25410.11. Higher order shear beam, gradient elasticity model 25910.12. Validity of the results for double-nanobeam systems 262Chapter 11. Surface Effects on the Natural Frequencies of Double-Walled Carbon Nanotubes 26911.1. Background 26911.2. Analysis 27111.3. Results and discussion 27911.4. Surface effects on buckling of nanotubes 28611.5. Summary 289Chapter 12. Summary and Directions for Future Research 291Appendix A. Elements of the Matrix A 297Appendix B. Elements of the Matrix B 299Appendix C. Coefficients of the Polynomial Equation [7.116] 301Appendix D. Coefficients of the Polynomial Equation [9.25] 303Appendix E. Coefficients of the Polynomial Equation [9.35] 305Appendix F. Coefficients of the Polynomial Equation [9.40] 307Appendix G. Coefficients of the Polynomial Equation [9.54] 311Appendix H. Coefficients of the Polynomial Equation [9.63] 313Appendix I. Coefficients of the Polynomial Equation [9.67] 315Appendix J. An Equation Both More Consistent and Simpler than the Bresse–Timoshenko Equation 319Bibliography 325Author Index 399Subject Index 415