The technique of Bloch expansions is exploited for composite materials with periodic structures made of linear piezoelectric and elastic constituents. The derivation is based on a variational formulation and an appropriate functional framework. While in the static limit the method provides homogenized electroelastic coefficients that coincide with those deduced from other homogenization techniques (asymptotic homogenization, gamma-convergence), in the dynamical framework it applies to a wide frequency spectrum and will, therefore, account for filtering properties of high interest in new piezoelectric signal-processing components.
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