Effective medium for time-varying frequency-dispersive acoustic metamaterials

The effective medium theory is a key concept in metamaterials, with a growing interest in the temporal effec-tive medium when the constitutive parameters are modulated with a period much shorter than the signal period. However, the effective medium with both frequency dispersion and time-varying resonating parameters is not clearly understood. In this work, we establish the temporal effective medium theory for acoustic metamaterials with time-varying frequency dispersion for compressibility. The formulas for the effective medium vary with the modulation of different resonance parameters and the transition from frequency-dispersive to-nondispersive regimes. Through experiments and theoretical models, we determine that time-varying resonance strength corresponds to the temporal average of compressibility beta, time-varying resonating frequency corresponds to the temporal average of 1/(beta-beta 0) in the frequency-dispersive regime, and time-varying modulation amplitude in the nondispersive regime corresponds to the temporal average of 1/beta. These results clarify the effective medium for frequency-dispersive time-varying metamaterials and have potential applications in different classical waves such as acoustics, elastodynamics, and electromagnetism for designing temporal functional devices.

Automated summary

This study establishes the temporal effective medium theory for acoustic metamaterials with time-varying frequency dispersion for compressibility. The formulas for the effective medium vary with different modulation parameters and the transition between dispersive and nondispersive regimes. The results have potential applications in designing temporal functional devices in classical waves such as acoustics, elastodynamics, and electromagnetism.