Mechanisms of bandgap formation in 2D single-phase phononic crystals with 4-fold rotational symmetry

We investigate the formation mechanisms of bandgaps (BGs) in 2D phononic crystals (PnCs) with 4-fold rotational symmetry, focusing on the symmorphic p4 and p4mm, and the nonsymmorphic p4gm plane symmetry groups. Based on those symmetry groups, we introduce families of designs that are straightforward to replicate. By exploring the coupling between Bragg scattering and local resonance mechanisms through a comprehensive parametric study, we demonstrate the feasibility of achieving extremely wide, complete omnidirectional BGs in single-phase PnCs. Numerical simulations and experimental results confirm the presence of strongly coupled BGs with superior attenuation properties for both P- and S-waves, particularly in designs with large resonators and thin connectors. We reveal an extremely wide 118% complete omnidirectional BG with remarkable attenuation of up to 80 dB after 3 rows of unit cells. Our study shows that the specific arrangement of connectors and resonators within the PnCs, analogous to masses and springs, plays a crucial role in the formation of strongly coupled resonant-Bragg BGs. Furthermore, the study challenges the conventional emphasis on symmetry in PnC design, suggesting that less sophisticated symmorphic designs can achieve comparable BG performance to their nonsymmorphic counterparts. This work contributes to the understanding of BG formation mechanisms in single-phase PnCs and offers guidelines for engineering enhanced vibration isolating devices.