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Updated: May 31, 2026
09:12
Functionalization of Single-walled Carbon Nanotubes with Thermo-reversible Block Copolymers and Characterization by Small-angle Neutron Scattering
Published on: June 1, 2016
A nonlocal shell model for mode transformation in single-walled carbon nanotubes
1School of Mechanical, Aerospace and Civil Engineering, Pariser Building, University of Manchester, PO Box 88, Manchester M60 1QD, UK. Department of Engineering Mechanics, College of Science, Chang'an University, Xi'an 710064, People's Republic of China.
Summary
This study establishes a nonlocal shell model for single-walled carbon nanotubes (SWCNTs), finding a negative second-order model is best. The research calibrates nonlocal length using molecular dynamics simulations for accurate vibration analysis.
Area of Science:
- Nanotechnology
- Materials Science
- Computational Mechanics
Background:
- Single-walled carbon nanotubes (SWCNTs) exhibit unique mechanical properties influenced by nanoscale effects.
- Understanding vibration modes and mode transformation is crucial for SWCNT applications.
- Existing models may not fully capture the nonlocal behavior of SWCNTs.
Purpose of the Study:
- To establish and validate a second-order strain gradient nonlocal shell model for SWCNTs.
- To investigate the effects of nonlocal parameters on vibration modes, specifically the radial breathing mode (RBM) and circumferential flexural modes (CFMs).
- To analyze mode transformation and internal resonance phenomena in SWCNTs.
Main Methods:
- Development of a second-order strain gradient nonlocal shell model.
- Calibration of nonlocal length using molecular dynamics (MD) simulations.
- Analysis of nonlocal length effects on RBM and CFM frequencies.
- Investigation of mode transformation and internal resonances.
Main Results:
- A negative second-order nonlocal shell model is identified as appropriate for SWCNTs.
- Nonlocal length is found to be dependent on vibration modes and the radius-to-thickness ratio.
- An average nonlocal length of approximately 0.1 nm is determined for RBM frequencies.
- Nonlocal lengths of 0.122-0.259 nm are indicated for mode transformation in armchair SWCNTs.
- Internal resonances (2:1 and 1:1) are observed, dependent on the model used.
- An effective thickness of ~0.1 nm is suggested for SWCNTs.
Conclusions:
- The validated nonlocal shell model accurately describes SWCNT vibration behavior.
- Nonlocal effects significantly influence SWCNT vibrational characteristics and mode transformations.
- The findings provide crucial parameters for accurate modeling and design of SWCNT-based devices.
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