Flexural-flexural-torsional Nonlinear Vibrations of Pre-twisted Rotating Beams with Asymmetric Cross-sections
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Bibliographic record
Abstract
The equations of nonlinear flexural-flexural-torsional vibrations of rotating beams with asymmetric cross-sections are derived. As the cross-section is asymmetric the centre of gravity and shear centre of a beam cross-section are not assumed to coincide. The nonlinear vibrations are expanded into flexural-torsional vibrational mode series. Using the Galerkin technique, the large-scale system of ordinary differential equations is derived. The non-linear modes are used to study teh free vibrations of a rotating beam, and the backbone curves of the free vibrations and the surfaces of the non-linear modes are also presented.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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