On the Application of Modified Finite Sine Transform to Structural Mechanics
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Bibliographic record
Abstract
The method of modified finite sine transform (MFST) was introduced to solve fourth‐order boundary value problems in structural mechanics. The analytical features and computational aspects of MFST were presented, including integral transforms of the derivatives of functions and the term‐by‐term differentiation of inverse MFST. For the simplicity of demonstrating the solution process, the cantilever beam was used in the discussion. Numerical results for transverse vibration based on the present method were compared and validated with existing results for natural frequencies. Although the present method is not superior to conventional finite sine transform method in one‐dimensional structures, it could be significantly efficient for two‐dimensional structures with asymmetric boundary conditions, especially including cantilever plates and other plates with only one free edge or two adjacent free edges.
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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