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Abstract: The paper studies the modes of vibrations of a lattice with rod-likeparticles, in a continuum model where the sites of the lattice are theconnections among strings and rigid rods. In these structures then,translational and rotational degrees of freedom are strongly coupled. We willdiscuss in particular two-dimensional lattices with auxetic-like behaviour.Auxetics are materials with a negative Poisson elastic parameter, meaning thatthey have a lateral extension, instead to shrink, when they are stretched. Weassume as -auxetic-like- two-dimensional structures, structures which do notcollapse, when stretched in one of the in-plane directions. The presence ofrigid rod-like particles in the lattice prevents the shrinking of the membrane.Complete bandgaps between acoustic and optical modes are observed in analogywith the behaviour of crystalline materials.



Author: A. Sparavigna

Source: https://arxiv.org/



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