Elastic wave propagation in self-similar and non-self-similar hierarchical two-dimensional square lattices

Abstract

In this talk, we examine the elastic wave propagation behavior of infinite two-dimensional self-similar and non-self-similar hierarchical square periodic lattices. Using finite element analysis, we calculate the dispersion curves of different hierarchical lattice structures along their irreducible Brillouin zone (IBZ) paths. The effects of similarity, geometrical symmetry, and material symmetry on bandgap generation are studied. The mechanisms responsible for bandgap generation are explained by studying the mode shapes for different characteristic length ratios. We show that material symmetry can help induce wave attenuation bandgaps at low frequencies. Further, we classify the P- and S-wave propagation modes and study the effect of similarity on the generation of polarized bandgaps. We demonstrate that controlling the hierarchical similarity provides a robust method for tailoring the dispersion characteristics of periodic lattice structures.