Invariant and energy analysis of an axially retracting beam
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Bibliographic record
Abstract
The mechanism of a retracting cantilevered beam has been investigated by the invariant and energy-based analysis. The time-varying parameter partial differential equation governing the transverse vibrations of a beam with retracting motion is derived based on the momentum theorem. The assumed-mode method is used to truncate the governing partial differential equation into a set of ordinary differential equations (ODEs) with time-dependent coefficients. It is found that if the order of truncation is not less than the order of the initial conditions, the assumed-mode method can yield accurate results. The energy transfers among assumed modes are discussed during retraction. The total energy varying with time has been investigated by numerical and analytical methods, and the results have good agreement with each other. For the transverse vibrations of the axially retracting beam, the adiabatic invariant is derived by both the averaging method and the Bessel function method.
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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