On acoustic band gaps in homogenized piezoelectric phononic materials

Abstract

We consider a composite medium made of weakly piezoelectric inclusions periodically distributed in the matrix which ismade of a different piezoelectricmaterial. Themediumis subject to a periodic excitation with an incidence wave frequency independent of scale ε of the microscopic heterogeneities. Two-scale method of homogenization is applied to obtain the limit homogenized model which describes acoustic wave propagation in the piezoelectric medium when ε → 0. In analogy with the purely elastic composite, the resulting model allows existence of the acoustic band gaps. These are identified for certain frequency ranges whenever the so-called homogenized mass becomes negative. The homogenized model can be used for band gap prediction and for dispersion analysis for low wave numbers. Modeling such composite materials seems to be perspective in the context of Smart Materials design