Small-scale computational vibration of carbon nanotubes : composite structure / Muzamal Hussain.
CNTs have a variety of applications because of their distinctive molecular structure and show unique electronic and mechanical properties because of their curvature. Nanotubes and micro-beams can be cited as one of the very applicable micro- and nano-structures in various systems, namely, sensing de...
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| Format: | eBook |
| Language: | English |
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River Publishers,
2023.
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| Series: | River Publishers series in mathematical, statistical and computational modelling for engineering.
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Table of Contents:
- Preface xi Acknowledgments xiii List of Figures xv List of Tables xix List of Notations xxi List of Abbreviations xxiii Abstract xxv 1 Introduction 1 1.1 Carbon Nanotube 1 1.2 Structure of CNTs 2 1.3 Types of CNTs 3 1.4 Properties of Carbon Nanotubes 4 1.5 Categories of CNT 5 1.6 Chirality Vector of Carbon Nanotubes 5 1.7 Outline of the Present Study 6 2 Single-walled Carbon Nanotubes Modeled as Flügge Shell Theory: Influences of Length-to-Diameter Ratios 11 2.1 Introduction 11 2.2 Theoretical Formation 15 2.2.1 Continuum Shell Theory 16 2.2.2 Flügge's shell theory 20 2.2.3 Solution scheme 21 2.2.4 Selection of displacement deformation functions 21 2.2.5 Derivation of generalized eigenvalue problem 24 2.2.6 Derivation of shell frequency equation 28 2.3 Result and Discussion 29 2.3.1 Vibration effect of length-to-diameter ratios of Armchair SWCNTs 31 2.3.2 Vibration effect of length-to-diameter ratio of zigzag SWCNTs 33 2.3.3 Vibration effect of length-to-diameter ratios of chiral SWCNTs 35 2.4 Conclusion 37 3 Accuracy of Stiffness on the Vibration of Single-walled Carbon Nanotubes: Orthotropic Shell Model 43 3.1 Introduction 44 3.2 Model-based Method 47 3.2.1 Orthotropic shell model 47 3.2.2 Relationships between strain and displacement 48 3.2.3 Relationships between stress and strain 49 3.2.4 Modal deformation displacements 52 3.3 Waves Propagation 53 3.4 Results and Discussion 54 3.4.1 Effect of stiffness on the vibration of armchair SWCNTs 56 3.4.2 Effect of stiffness on the vibration of zigzag SWCNTs 58 3.4.3 Effect of stiffness on the vibration of chiral SWCNTs 61 3.5 Conclusions 63 4 Donnell Shell Theory Formulation - Single-walled Carbon Nanotubes: Frequency Assessment via Height-to-Diameter Ratios 69 4.1 Introduction 70 4.2 Mathematical Formulation 72 4.2.1 Equation of motion using shell model 72 4.3 Numerical Approach 74 4.3.1 Modal displacement form 74 4.4 Numerical Results 75 4.4.1 Parametric study 75 4.4.2 Validation 76 4.4.3 Effect of height-diameter ratio on the vibration of armchair single-walled carbon nanotubes 78 4.4.4 Effect of height-diameter ratio on the vibration of zigzag single-walled carbon nanotubes 80 4.4.5 Effect of height-diameter ratio on the vibration of chiral single-walled carbon nanotubes 82 4.5 Conclusions 84 5 Impact of Poisson's Ratios on the Vibration of Singlewalled Carbon Nanotubes: Prediction of Frequencies through Galerkin's Technique 89 5.1 Introduction 90 5.2 Structural Analysis and Modeling 92 5.2.1 Theoretical formulation 92 5.3 Application of Sander's Shell Theory 93 5.4 Derivation of Shell Governing Equations 97 5.5 Modal Displacement Forms 98 5.6 Use of the Galerkin Method 99 5.7 Parametric Study, Validation, and Discussion of Results 101 5.7.1 Influence of Poisson's ratio on the Vibration of Armchair SWCNTs 102 5.7.2 Influence of Poisson's ratio on the vibration of zigzag SWCNTs 105 5.7.3 Influence of Poisson's ratio on the vibration of chiral SWCNTs 107 5.8 Conclusions 110 6 Wave Propagation in Single-walled Carbon Nanotubes via Euler Beam Theory 113 6.1 Introduction 114 6.2 Theoretical Formulation 117 6.2.1 Algorithm description 118 6.2.2 Numerical technique 120 6.2.3 Boundary conditions 121 6.3 Modeling Results and Discussions 122 6.3.1 Evaluation parameters 122 6.3.2 Modeling validation 122 6.3.3 Effect of fundamental natural frequencies against density on vibration of armchair SWCNTs 123 6.3.4 Effect of Fundamental Natural Frequencies against Density on Vibration of Zigzag SWCNTs 126 6.3.5 Effect of fundamental natural frequencies against density on vibration of chiral SWCNTs 128 6.4 Conclusion 131 7 Concluding Remarks/Summary/Future Recommendation 135 7.1 Conclusion 135 7.2 Future Recommendation 138 Appendices 139 Appendix 2.1 139 Appendix 2.2 139 Appendix 3.1 141 Appendix 4.1 142 Index 143 About the Author 145.