Sub-preferential rotational wave beaming in structurally rhombus re-entrant honeycombs

Rotational waves frequently manifest in micro-structured materials and are often coupled with classical shear or longitudinal wave modes. In this study, a distinctive isolated optical branch, exhibiting very high polarization index related to joint rotation motion, is found in dispersion diagram of elastic wave propagation in structurally rhombus re-entrant honeycomb (SSRH). Through an analysis of group velocity, we further explore the wave beaming of the rotational wave propagation within the SRRH, and intriguingly, observe the emergence of sub-preferential wave beaming occurring along the short diagonal directions. This dynamic anisotropic phenomenon stems from the intricate interplay between wave frequency and structural topology. To elucidate the underlying dynamic anisotropy of rotational waves, we propose a simple rigid-spring model and derive a modulation function that precisely captures the intricate frequency-structure coupling behavior. The obtained modulation function unveils the formation of sub-preferential directions of the rotational wave within the SRRH.