Bandgap tuning in bioinspired helicoidal composites

The dispersion of waves in helicoidal layered composites is investigated using propagation matrices and the Bloch's theorem to represent the layered nature and periodicity of the material, respectively. Dispersion relations are found solving the resulting eigenvalue problems. Concrete numerical investigations are made for a collection of transversely isotropic materials. The influence of the anisotropy (or directionality) of the constituent materials for each layer is presented in a qualitative and quantitative fashion. Dispersion curves are presented for some of these materials, and for different helicoidal configurations. We determined the size of the first bandgap for different anisotropy levels, showing that the most important parameter for shear wave filtering is the ratio of elastic constants C44/C66, and thus the anisotropy of the S waves in each layer is more interesting than the anisotropy for quasi–S and quasi–P ones. Considering the results, we can design for the appearance and size of the bandgaps by careful selection of the materials that constitute the layers of the composites.