Inner acoustic resonance for long wave propagation in periodic piezoelectric composites

•We investigate macroscopic models describing waves in piezoelectric composites.•At a given frequency, acoustic wavelengths are smaller than electromagnetic ones.•We consider in particular long electromagnetic wavelengths.•They can correspond to acoustic wavelengths of the heterogeneity size.•It results in an acoustic resonance at the heterogeneity scale.

We investigate equivalent macroscopic models describing long wave propagation in periodic piezoelectric composite, with a particular attention to acoustic resonance. ”Long” means that wavelength are much larger than the heterogeneity scale characteristic length. These macroscopic models are obtained by using the method of asymptotic expansions, which is based on the systematic use of the existence of a separation of scales. We make full use of the evidence that piezoelectricity couples two very different phenomena: a stiff one, the electromagnetic wave propagation, and a softer one, the acoustic wave propagation. For a given frequency, the electromagnetic wavelength is very much larger than the acoustic wavelength. The method of asymptotic expansions is well suited for considering such a contrast through dimensionless numbers. It results in typical models of different structures: model I for acoustic long wave propagation; model II for electromagnetic long wave propagation which shows inner acoustic resonance; model III for acoustic resonance in presence of a quasi-electrostatic excitation. The domain of validity of the different models is clearly shown.