A new mathematical model for resonant-column measurements including eddy-current effects
Bibliographic record
Abstract
Wave velocity and attenuation are commonly studied in the laboratory with the resonant-column device (American Society for Testing and Materials standard), which is driven by a set of coils and magnets. This paper presents a new and robust mathematical model of the electromechanical resonant-column system. The model is used to compute various transfer functions. Eddy currents, a new source of damping identified in the resonant-column device, introduce damping proportional to the velocity of the magnets. Eddy-current damping is considered in the mathematical model. A testing program is devised to calibrate the resonant column with three aluminum probes. Experimental and theoretical results show an excellent agreement (4% maximum error). Exploratory results are presented for a dry-sand specimen. A resonant-column device is modified to demonstrate the significant effect of the induced voltage (electromotive force (EMF)) on damping ratio if tests are not based on current measurements. Free-vibration tests on aluminum specimens and a dry-sand specimen show a significant effect of the induced EMF (up to 400% increase in damping for the sand specimen). The induced voltage depends on the resonant frequency and damping of the specimen. In the case of aluminum probes, eddy-current damping represents 20150 times the material damping of the specimen. Preliminary results on dry sand show that eddy-current damping represents up to a 15% increase in damping ratio. However, the magnitude of eddy-current damping depends on the configuration and materials used in the resonant-column device. The smaller the damping ratio of the specimen is, the more important the eddy-current damping becomes.Key words: damping, eddy currents, mechanical waves, resonant-column device, shear modulus, wave velocity.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".