Bibliographic record
Abstract
Locally resonant acoustic materials were proposed to control sound using structures with feature size orders of magnitude smaller than the acoustic wavelength in air. Millimeter-sized resonators over the audible frequency range typically consist of dense cores coupled to stiff shells through elastically soft material. Using a rigid core-shell approximation (RCSA), we analytically derive the frequency-dependent, effective inertial quantities for the fundamental translational and rotational resonances of such core-shell resonators. The effective inertia is expressible in closed form by elementary functions, enabling a mapping of the low-frequency physics to a simple model involving a point mass or a rod harmonically coupled to a box. We present an effective inertia-spring tensor (EIST) 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 EIST model is a generalization of the widely quoted point-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 and three-dimensional models, that our simple representation accurately describes exact phononic band structures involving coupled translational and rotational modes, in close agreements with the finite-element method. The existence and the frequency range of local resonance band gaps are predicted by the concurrence of negative effective mass and moment of inertia. A large local resonance gap may occur in spectral proximity to a distinct gap arising from Bragg scattering. Our model is generalized to complex dumbbell-shaped resonators, revealing a dense collection of flat ``slow sound'' bands near the local resonance band gap. We demonstrate that thin claddings of such locally resonant, phononic crystals, of only three to five unit cells in thickness, can effectively prevent sound transmission, by a combination of reflection and absorption, over much of the audible spectrum. Moreover, frequency-selective sound transmission can be enabled by engineering waveguide channels that transmit sound through the local resonance gap, the Bragg gap, or both. This offers a path to sound-sculpting claddings that can surround a noise-generating source.
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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) | 0.000 | 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 | 0.000 |
| Open science | 0.000 | 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".