Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes
Abstract
:1. Introduction
2. Sanders–Koiter Shell Theory for SWCNTs
3. Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model
4. Force and Moment Resultants
5. Equations of Motion
6. Solution Method
7. Numerical Results
7.1. Validation of the Anisotropic Elastic Shell Model
7.2. Effects of Nonlocal and Material Parameters
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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Carbon–carbon bond length, a (nm) | 0.142 |
Carbon–carbon bond elongation, Kρ (nN/nm) | 742 |
Carbon–carbon bond angle variance, Kθ (nN·nm) | 1.42 |
Equivalent thickness, h (nm) | 0.0665 |
Equivalent mass density, ρ (kg/m3) | 11,700 |
SWCNT radius, R (nm) | 1.34 |
Natural Frequency, ωRBM (cm−1) | Difference (%) | ||
---|---|---|---|
Chirality Indices (n, m) | Anisotropic Elasticity Model (Sanders’s Shell Theory) | Molecular Dynamics Simulation [25] | |
(10, 0) | 294.310 | 290.810 | 1.20 |
(6, 6) | 284.460 | 278.450 | 2.16 |
(12, 0) | 245.868 | 242.576 | 1.36 |
(7, 7) | 244.074 | 239.020 | 2.11 |
(8, 8) | 213.709 | 209.323 | 2.10 |
(14, 0) | 211.067 | 207.980 | 1.48 |
(16, 0) | 184.870 | 181.960 | 1.60 |
(10, 10) | 171.104 | 167.644 | 2.06 |
(18, 0) | 164.443 | 161.773 | 1.65 |
(20, 0) | 148.073 | 145.577 | 1.71 |
(12, 12) | 142.650 | 139.778 | 2.05 |
(25, 0) | 118.551 | 116.439 | 1.81 |
(15, 15) | 114.161 | 111.878 | 2.04 |
(30, 0) | 98.835 | 97.013 | 1.88 |
(18, 18) | 95.153 | 93.253 | 2.04 |
(33, 0) | 89.865 | 87.507 | 2.69 |
(20, 20) | 85.645 | 83.935 | 2.04 |
Natural Frequency, ωRBM (cm−1) | Difference (%) | ||
---|---|---|---|
Chirality Indices (n, m) | Isotropic Elasticity Model (Sanders’s Shell Theory) | Molecular Dynamics Simulation [25] | |
(10, 0) | 299.083 | 290.810 | 2.84 |
(6, 6) | 288.075 | 278.450 | 3.46 |
(12, 0) | 249.447 | 242.576 | 2.83 |
(7, 7) | 246.812 | 239.020 | 3.26 |
(8, 8) | 215.923 | 209.323 | 3.15 |
(14, 0) | 213.955 | 207.980 | 2.87 |
(16, 0) | 187.002 | 181.960 | 2.77 |
(10, 10) | 172.925 | 167.644 | 3.15 |
(18, 0) | 166.287 | 161.773 | 2.79 |
(20, 0) | 149.741 | 145.577 | 2.86 |
(12, 12) | 144.037 | 139.778 | 3.05 |
(25, 0) | 119.753 | 116.439 | 2.85 |
(15, 15) | 115.183 | 111.878 | 2.95 |
(30, 0) | 99.772 | 97.013 | 2.84 |
(18, 18) | 96.003 | 93.253 | 2.95 |
(33, 0) | 90.665 | 87.507 | 3.61 |
(20, 20) | 86.396 | 83.935 | 2.93 |
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Strozzi, M.; Elishakoff, I.E.; Bochicchio, M.; Cocconcelli, M.; Rubini, R.; Radi, E. Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes. C 2024, 10, 24. https://doi.org/10.3390/c10010024
Strozzi M, Elishakoff IE, Bochicchio M, Cocconcelli M, Rubini R, Radi E. Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes. C. 2024; 10(1):24. https://doi.org/10.3390/c10010024
Chicago/Turabian StyleStrozzi, Matteo, Isaac E. Elishakoff, Michele Bochicchio, Marco Cocconcelli, Riccardo Rubini, and Enrico Radi. 2024. "Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes" C 10, no. 1: 24. https://doi.org/10.3390/c10010024