Medium frequency vibration modeling of cracked plates using hierarchical trigonometric functions
Bibliographic record
Abstract
A modeling tool is proposed to describe the vibration behavior of pristine and damaged plates in the medium frequency range (below 10 kHz). This tool is intended to provide a platform for the development and assessment of damage detection algorithms for aircraft structural health monitoring applications. The proposed analytical model employs a Hierarchical Trigonometric Function Set (HTFS) to characterize homogeneous plates with through cracks. This approach takes advantage of the very high order of stability of the HTFS [O. Beslin and J. Nicolas, J. Sound Vib. 202, 633–655 (1997)] to approximate the effects of a small crack in a plate for all combinations of classical boundary conditions (e.g., CFSC, CCFF, FSFS). The model is first presented and then assessed for healthy and cracked CCCC plates with eigenvalues and eigenmodes presented in the literature. For a healthy square plate, numerical results provide good agreement up to the 1000th mode while, for a cracked rectangular plate, good agreement is obtained up to the 3rd mode, corresponding to the highest mode order available in the literature. Wave propagation simulation obtained from HTFS shows the scattering around the cracks in the plates. Experimental validation of the model is conducted both in frequency and time domains for healthy and cracked plates. [Work supported by the Consortium for Research and Innovation in Aerospace in Quebec (CRIAQ) and Defence R&D Canada.]
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".