Theory 010/Physics & Matter /Acoustic metamaterials
Bandgaps Follow the Mass Ratio
High quality factors are prized. The gap may care more about how much mass is moving.
The width of a locally resonant metamaterial bandgap is set by the ratio of resonator mass to host mass rather than by resonator quality factor, so a heavy, lossy resonator can outperform a light, high-Q one.
01The evidence
Locally resonant metamaterials produce bandgaps far below the Bragg limit, with gap width varying across designs in ways that do not track damping alone.
02The tension
Design intuition favours low damping and high Q, and the gap is modelled from the resonance. Mass loading is treated as a tuning parameter rather than the determinant of width.
03The mechanism
A local resonator couples to the host through its mass. The depth and width of the resulting gap depend on how much of the host's effective mass the resonator can move, which is the mass ratio.
Damping broadens but also shallows the resonance, so the net effect on gap width is a trade-off that the mass ratio sets.
04What this is not
Q-driven design maximises resonance sharpness. This maximises coupled mass, which predicts wide gaps from lossy heavy resonators.
05Predictions
- P1Gap width should scale with mass ratio.
- P2Heavy lossy resonators should outperform light high-Q ones.
- P3Gap depth should trade against width through damping.
06Refutation
Gap width tracking Q at fixed mass ratio would restore the resonance account.
07What it changes
It would change how metamaterial absorbers are designed.