The DOI matches its Crossref record.
Oscillations of a thin hollow cylinder: Carbon nanotubes
Abstract
The classical vibrational modes are calculated for a thin-walled hollow cylinder of isotropic material. An analytical solution is obtained for all of the modes. The results are applied to calculate the low-frequency vibrational modes of a single-wall carbon nanotube. Analytical formulas are obtained for the Raman frequencies, and for the velocities of acoustical modes.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Theory of Electronic States and Transport in Carbon Nanotubes
Ando, T. (2005) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.74.777 · Cited by 893
Vibrations of carbon nanotubes and their composites: A review
Gibson, R. F., Ayorinde, E. O., & Wen, Y.-F. (2007) · Composites Science and Technology · doi:10.1016/j.compscitech.2006.03.031 · Cited by 530
Mechanics of Pipes Conveying Fluids—Part II: Applications and Fluidelastic Problems
Ibrahim, R. A. (2011) · Journal of Pressure Vessel Technology · doi:10.1115/1.4001270 · Cited by 135
Metadata
- Authors
- Mahan, G. D.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2002-05-23
- Volume
- 65
- Issue
- 23
- ISSN
- 0163-1829 (ISSN-L)
- 1095-3795
- OpenAlex
- W2061962961
- Cited by
- 189
- References
- 0
- FWCI
- 8.66
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Oscillations of a thin hollow cylinder: Carbon nanotubes. https://app.cochat.ai/papers/10.1103/physrevb.65.235402
- The paper
- Mahan, G. D. (2002). Oscillations of a thin hollow cylinder: Carbon nanotubes. Physical Review B. https://doi.org/10.1103/physrevb.65.235402
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
