The power series technique and detection of zero-group velocity Lamb waves in a functionally graded material plate
Bibliographic record
Abstract
This paper presents a technique for measuring the variation of the material properties along the thickness in a functionally graded material (FGM) plate. To investigate the propagation behavior of Lamb waves in a thermal stress relaxation type FGM plate with material parameters that vary continuously along the thickness, the power series technique, which has been proved to have good convergence and high precision, is employed for theoretical derivations. The method exploits the resonance at the minimum frequency of the S1 - zero group velocity (ZGV) mode. At this minimum frequency (f0), the group velocity vanishes, whereas the phase velocity remains finite. The numerical results also reveal differences between the ZGV frequency in the FGM plate and the corresponding frequency in a homogenous plate. In terms of results, we find that the in-plane and out-plane displacements are different between Al-rich and Si-rich surfaces. The plots of the involved stresses within the plate are added to check the performed calculations. Besides, the study covers the sensitivity of S1-ZGV resonance frequency to the FGM character and any slight variation of the plate thickness. All these results give theoretical guidance not only for experimental measurement of material properties but also for nondestructive evaluation using an ultrasonic wave generation device.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".