Dispersion properties in homogenized piezoelectric phononic materials

Abstract eng:
We consider a composite medium made of weakly piezoelectric inclusions periodically distributed in the matrix which is made of a different piezoelectric material. The medium is subject to a periodic excitation with an incidence wave frequency independent of scale ε of the microscopic heterogeneities. Two-scale method of homogenization was 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 is featured by 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 of these types of composite materials seems to be perspective in the context of Smart Materials design.

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