Free vibration of multiwall carbon nanotubes
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Bibliographic record
Abstract
A multiple-elastic shell model is applied to systematically study free vibration of multiwall carbon nanotubes (MWNTs). Using Flugge [Stresses in Shells (Springer, Berlin, 1960)] equations of elastic shells, vibrational frequencies and associated modes are calculated for MWNTs of innermost radii 5 and 0.65 nm, respectively. The emphasis is placed on the effect of interlayer van der Waals (vdW) interaction on free vibration of MWNTs. Our results show that the interlayer vdW interaction has a crucial effect on radial (R) modes of large-radius MWNTs (e.g., of the innermost radius 5 nm), but is less pronounced for R modes of small-radius MWNTs (e.g., of the innermost radius 0.65 nm), and usually negligible for torsional (T) and longitudinal (L) modes of MWNTs. This is attributed to the fact that the interlayer vdW interaction, characterized by a radius-independent vdW interaction coefficient, depends on radial deflections only, and is dominant only for large-radius MWNTs of lower radial rigidity but less pronounced for small-radius MWNTs of much higher radial rigidity. As a result, the R modes of large-radius MWNTs are typically collective motions of almost all nested tubes, and the R modes of small-radius MWNTs, as well as the T and L modes of MWNTs, are basically vibrations of individual tubes. In particular, an approximate single-shell model is suggested to replace the multiple-shell model in calculating the lowest frequency of R mode of thin MWNTs (defined by the innermost radius-to-thickness ratio not less than 4) with relative errors less than 10%. In addition, the simplified Flugge single equation is adopted to substitute the exact Flugge equations in determining the R-mode frequencies of MWNTs with relative errors less than 10%.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it