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We examine some unusual wave propagation characteristics related to auxetic systems represented by continuum isotropic materials and hexagonal chiral lattices with and without active piezoelectric actuation. We show for the first time a peculiar singularity in the ratio between reflected P and S waves in Rayleigh‐wave type propagation for auxetic isotropic materials, which has been otherwise observed only in at least bi‐phase material systems. The other unusual phenomenon is a strong increase of the pass‐stop band frequencies in hexachiral lattices with piezoelectric materials, with no change of the shear‐wave type otherwise occurring in pristine lattice with no piezoelectric contribution.

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