Clustered Natural Frequencies in Multi-Span Beams with Constrained Characteristic Functions
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Bibliographic record
Abstract
A study of the natural frequencies and mode shapes of a multi-span beam is carried out by introducing constrained beam characteristic functions. The conventional method used for the dynamic analysis of such a beam is to consider span-wise characteristic function solution and then to solve it by using compatibility conditions such as the continuity in the a slope and bending moment at the intermediate supports and boundary conditions at the ends. In the method proposed here, the matrix size is reduced and, if the support conditions are symmetric about the midpoint, the symmetry and anti-symmetry conditions at the midpoint can be conveniently exploited for computational economy. The natural frequencies occur in clusters, each one containing the number of natural frequencies equal to the number of spans. The results are presented and discussed.
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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