Effective medium for time-varying frequency-dispersive acoustic metamaterials
Xinghong Zhu, Hong‐Wei Wu, Yue Zhuo, Ziling Liu, Jensen Li
Abstract
The effective medium theory is a key concept in metamaterials, with a growing interest in the temporal effective 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 \ensuremath{\beta}, time-varying resonating frequency corresponds to the temporal average of $1/(\ensuremath{\beta}\text{--}{\ensuremath{\beta}}_{0})$ in the frequency-dispersive regime, and time-varying modulation amplitude in the nondispersive regime corresponds to the temporal average of 1/\ensuremath{\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.