Homogenized phononic plates and wave dispersion

Abstract eng:
We consider the problem of wave propagation in periodically heterogeneous composite plates with high contrasts in elastic coefficients. The unfolding method of homogenization is applied to obtain limit plate models. Due to the high contrast ansatz in scaling the elasticity coefficients of compliant inclusions, the dispersion properties are retained in the limit when the scale of the microstructure tends to zero. We study two plate models based on the Reissner-Mindlin theory and on the Kirchhoff-Love theory. We show that, when the size of the microstructures tends to zero, the limit homogeneous structure presents, for some wavelengths, a negative “mass density” tensor. This means that there exist intervals of frequencies in which there is no propagation of elastic waves, the so-called band-gaps.

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