Anisotropy-induced wave steering in periodic linear and nonlinear lattices

Structural lattice configurations can be designed with tailored topologies which provide them with unusual behaviors, such as negative bulk modulus, negative Poisson's ratios, or extreme anisotropy\footnote{M. Ruzzene et al. Phisica Status Solidi B, \textbf{242}, 665 (2005)}. The latter is of particular relevance to explore the inherent anisotropic behavior of periodic lattices as a design paradigm for wave guiding and steering applications. The equivalent material anisotropy of square and skew periodic lattices is investigated through the application of Bloch's theorem\footnote{Bloch F., Z. Physik \textbf{52}, 555 (1928)} to the finite element discretization of the representative unit cell. The in-plane directions of wave propagation are determined through detailed analysis of the longitudinal and shear wave velocities, and verified through full-field wave propagation simulations. Similar wave behaviors are investigated analytically and experimentally for multilayer composite panels with anisotropic lay-ups in order to demonstrate the feasibility of micro structural design as an effective approach for wave management.