Nonlinear Vibrations of a SWCNT with Geometrical Imperfection Using Nonlocal Elasticity Theory
Bibliographic record
Abstract
The nonlinear free vibration and frequency veering of a single wall carbon nanotube (SWCNT) based on nonlocal elasticity theory is studied and investigated in this paper. The carbon nanotubes (CNT) is assumed to have an imperfection modeled as half sine and clamped at both ends. The Euler-Bernoulli Beam and Hamilton’s principle were used to derive the nonlinear equation of motion of the SWCNT. The effect of; nonlocal elasticity, geometric initial rise/imperfection, and the effect of the axial force induced by mid-plane stretching are accounted for in the derivation of the nonlinear mathematical model of the CNT. The governing partial differential equation includes quadratic and cubic nonlinearities due to the initial imperfection and the mid-plane stretching. The derived equation of motion is discretized using the assumed mode method by inserting the exact linear eigen mode shape. The resulting nonlinear temporal equation was solved using the method of multiple scales (MMS) to obtain results for the nonlinear natural frequencies of the first three modes of vibrations, for different values of rise/imperfection amplitude, and for different values of the nonlocal parameter. The results are presented in non-dimensional characteristic curves to show the effect of variation of rise/imperfection amplitude and nonlocal parameter on the vibrational behavior of the CNT.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".