Chaotic and periodic vibration of a carbon nanotube supported by nonlinear foundation
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Bibliographic record
Abstract
The nonlinear vibrations and chaotic motion of a carbon nanotube subjected to axial loads and rested on a Winkler and Pasternak foundation are studied. It is assumed that the carbon nanotube is simply-supported at both ends. The governing equation of motion for the nanotube and foundation system using the Euler-Bernoulli beam theory is developed. The Galerkin method is considered for the solution of the governing equation to obtain the nonlinear ordinary differential equation of the system. The multiple time scale method is utilized to find the frequency response of the system. The bifurcation diagram, phase-plane trajectories and Poincaré section are considered to identify the chaotic region of oscillations of carbon nanotube.
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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