Effective inertia spring tensor model for acoustic materials with coupled local resonances
Bibliographic record
Abstract
We present a simple physical picture and precise model for the low-frequency acoustic modes of phononic crystals with multiple local resonances within each unit cell and their coupling to spatially separated resonators. The physical picture is a generalization of the widely quoted mass-in-a-box representation of resonant acoustic metamaterials. Our model consists of an array of frequency-dependent effective masses and moments of inertia coupled to near and distant neighbors by a wave-vector-dependent effective spring constant matrix. We demonstrate, using several two-dimensional models, that our simple representation accurately recaptures exact phononic band structure involving coupled translational and rotational modes. Our simplified but precise description is ideally suited for resonators consisting of multiple rigid cores and shells embedded in a softer elastic background. This enables a rich spectrum of acoustic modes and band gaps at audible frequencies, using millimeter to centimeter scale resonators. Our model is readily generalized to three-dimensional phononic crystals. It is suggested that suitable modifications of the spring tensor may enable description of disordered resonant acoustic media.
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".