Engineering Perspective of Spin Phenomena in Elastic Media

In phononics, spin can be understood as angular momentum arising from a circulating energy flow. In beam structural elements, elastic spin can be generated through combined external shear forces and bending moments with a particular amplitude ratio and phase difference. Previous studies have shown that this combination of external actions, referred to as chiral excitations, can induce wave steering in homogeneous beams. In this work, we explore the directional propagation of elastic waves in both homogeneous and periodic beams (phononic crystals). We derive an analytical expression for the shear-force-to-bending-moment ratio that enables bending wave steering at a specific frequency. Numerical simulations using the spectral element method demonstrate the effects of chiral excitation. Additionally, we investigate the influence of chiral excitations on both conventional and topological phononic crystal beams. Our findings reveal that while chiral forces induce spin effects, topological modes at the interface of two phononic crystals with distinct Zak phases dominate the wave dynamics, prevailing over the spin-induced effects.