Explicit Vibration Formulas Applicable to Timber Plates with Free and Simply Supported Edges
Bibliographic record
Abstract
Advances in research and development have led to the application of high-strength timber plates to flooring-slab construction. It is envisaged that floors built from timber plates will have different vibration behavior from conventional joisted floors. In this paper, explicit formulas are developed based on a matrix formulation that links both the symmetric and antisymmetric vibration modes of orthotropic plates. The developed solution can be used for the dynamic analyses of orthotropic timber floor slabs. The solution presented in this paper overcomes limitations associated with previous solutions by eliminating the need for approximate series expansions for solving the characteristic equations. Its application is demonstrated by considering responses of plates with all or two simply supported edges. The new solutions agree closely with classical and Finite-Element Method (FEM) solutions, as well as with the experimental results for Cross-Laminated Timber (CLT) plates. The advantage of the new approach versus alternatives is a combination of accuracy and computational efficiency.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| 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 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".