Anisotropy-induced broadband stress wave steering in periodic lattices

Abstract

This paper investigates two-dimensional periodic lattices as a means to induce strongly directional stress wave propagation in solids in the low-frequency broadband regime. The real 2D structure of the lattice is considered as opposed to traditional truss-like approaches, allowing the characterization of the system seamlessly between the extremes of grid-like systems, porous systems, and a continuum material. Wave directionality in structural lattices is associated to their effective anisotropic mechanical properties. When the wavelength of deformation is larger than the representative unit cell, the system behaves as an equivalent medium with orthotropic properties that are correlated to the lattice skewness and void volume fraction. Polar plots of wave velocities, computed through the application of Bloch’s theorem, provide insights into the effective anisotropy and wave directionality (or “steering”) of the structure. Such directional response is also correlated to the stiffness properties of an equivalent medium by means of proper homogenization techniques. The effects of the resulting anisotropy on wave propagation are also illustrated through wave propagation simulations for problems involving both harmonic excitations and impulsive loads.