Dual audible-range band gaps in three-dimensional locally resonant phononic crystals
Bibliographic record
Abstract
We describe a simple and transparent physical model for local acoustic resonances and their interactions in three-dimensional phononic crystals. The widely quoted point-mass-in-a-box representation of acoustic resonators is systematically generalized to an extended rigid body connected to massive springs, exhibiting multiple coupled local resonances. Millimeter-sized acoustic resonators over the audible frequency range typically consist of dense cores coupled to stiff shells through elastically soft material. When the local resonator is small compared to the acoustic wavelength, an elastostatic equilibrium approximation yields closed-form rational functions for its frequency-dependent, effective mass and moment of inertia. Our representation allows intuitive and quantitative analyses of the coupled acoustic modes of lattices of interacting resonators. 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. The band structure and density of states are determined by solving computationally inexpensive $6\ifmmode\times\else\texttimes\fi{}6$ matrix eigenvalue equations. These agree with the exact band structures obtained by finite-element method within $3.71%$, $2.32%$, and $2.38%$ errors for the simple cubic, body-centered cubic, and face-centered cubic arrangements of the resonators, respectively. Our model enables precise design of locally resonant phononic crystals with large dual band gaps spanning a significant fraction of the audible spectrum. By increasing the mass contrast between the core and the shell in spherical resonators, we demonstrate, using a specific phononic crystal, a local resonance band gap with $126.7%$ gap-to-midgap ratio. Our model is further extended to a lattice of dumbbell-shaped resonators, resulting in a dense collection of flat bands over a narrow, predetermined frequency range.
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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 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| 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".