Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory
Abstract
:1. Introduction
2. Problem Formulation
2.1. Timoshenko Beam Model for Vibration of Curved Single-Walled Carbon Nanotubes (SWCNTs)
2.2. Nonlocal Theory of Nano-Beams
2.3. Derivation of Nonlocal Governing Equations of Motion
2.4. Differential Quadrature Solution Procedure
3. Numerical Results and Discussions
3.1. Results Verification
3.2. Geometric Imperfection Function
3.3. Nonlinear Vibration of Curved SWCNTs
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
CNTs | Carbon Nano Tubes |
DQ | Differential Quadrature |
MD | Molecular Dynamics |
NEMS | Nano Electro Mechanical System |
SWCNTs | Single-Walled Carbon Nano Tubes |
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H–H | C–C | C–H | |||||||
---|---|---|---|---|---|---|---|---|---|
Ref. [35] | Ref. [36] | Present | Ref. [35] | Ref. [36] | Present | Ref. [35] | Ref. [36] | Present | |
1.0 | 1.118 | 1.118 | 1.1181 | 1.0295 | 1.0283 | 1.0295 | 1.0641 | 1.0582 | 1.0593 |
2.0 | 1.4141 | 1.4135 | 1.4143 | 1.1127 | 1.1105 | 1.1128 | 1.2318 | 1.215 | 1.2182 |
3.0 | 1.8026 | 1.8027 | 1.8029 | 1.2377 | 1.2336 | 1.2378 | 1.4603 | 1.4368 | 1.4416 |
4.0 | 2.2359 | 2.2361 | 2.2363 | 1.3920 | 1.3856 | 1.3921 | 1.7210 | 1.6822 | 1.7026 |
5.0 | 2.6923 | 2.6925 | 2.6928 | 1.5659 | 1.5574 | 1.5660 | 1.9995 | 1.9180 | 1.9862 |
μ | H–H | C–C | C–H | ||||||
---|---|---|---|---|---|---|---|---|---|
Ref. [37] | Ref. [22] | Present | Ref. [37] | Ref. [22] | Present | Ref. [37] | Ref. [22] | Present | |
0.0 | 3.0929 | – | 3.0929 | 4.4491 | – | 4.4491 | 3.7845 | – | 3.7844 |
0.1 | 3.0243 | 3.0210 | 3.0210 | 4.3471 | 4.3269 | 4.3269 | 3.6939 | 3.6849 | 3.6849 |
0.3 | 2.6538 | 2.6385 | 2.6385 | 3.7895 | 3.7032 | 3.7032 | 3.2115 | 3.1724 | 3.1724 |
0.5 | 2.2867 | 2.2665 | 2.2665 | 3.2420 | 3.1372 | 3.1371 | 2.7471 | 2.6982 | 2.6980 |
0.7 | 2.0106 | – | 1.9899 | 2.8383 | – | 2.7327 | 2.4059 | – | 2.3569 |
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Eshraghi, I.; Jalali, S.K.; Pugno, N.M. Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory. Materials 2016, 9, 786. https://doi.org/10.3390/ma9090786
Eshraghi I, Jalali SK, Pugno NM. Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory. Materials. 2016; 9(9):786. https://doi.org/10.3390/ma9090786
Chicago/Turabian StyleEshraghi, Iman, Seyed K. Jalali, and Nicola Maria Pugno. 2016. "Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory" Materials 9, no. 9: 786. https://doi.org/10.3390/ma9090786