On acoustic wave beaming in two-dimensional structural lattices

Abstract

We discuss directional energy flow, often referred to as wave beaming, in two-dimensional periodic truss lattices under infinitesimal harmonic excitation. While the phenomenon of directional wave guiding is well-known and commonly treated in the context of dispersion relations, the theoretical and computational tools to predict beaming are limited, which is why a fundamental understanding for complex lattices is incomplete. Here, we present a new strategy to identify partial band gaps and wave beaming in a simple fashion, covering wide frequency ranges and distinguishing in-plane and out-of-plane vibrational modes in lattices composed of linear elastic Euler-Bernoulli beams. By calculating group velocities that provide insight into the frequency-dependent directional energy flow, we show that dispersion surfaces overlap in frequency and beaming direction, elucidating the need to consider multiple surfaces when predicting global system response – in contrast to many prior approaches that focused on the lowest surface(s) individually. These concepts are demonstrated for three examples of two-dimensional structural lattices (of rectangular, sheared, and hexagonal architecture), for each of which we study the influence of geometry on wave dispersion. Direct numerical simulations validate directional energy flow predictions, demonstrate directional frequency dispersion, and highlight conventional dispersion analysis limitations.