ENHANCED VIBRATION ATTENUATION IN P4GM PHONONIC CRYSTALS VIA COUPLED BRAGG AND LOCAL RESONANCE BANDGAPS

Phononic crystals (PnCs) are periodic materials based on particular geometric designs that create a periodic impedance contrast. PnCs can attenuate elastic waves at various frequencies, offering unique acoustic capabilities. The phononic band structure of a PnC is typically determined by its geometry, mechanical properties, and symmetry. Higher symmetries lead to an increased likelihood of achieving a complete omnidirectional phononic bandgap (BG) – a range of frequencies that are not propagated but attenuate exponentially for all wavevectors due to Bragg scattering, local resonance (hybridization), or weak elastic coupling mechanisms. In this study, we investigate how complex symmetries and geometric features push the limits of complete omnidirectional BGs in single-phase PnCs by examining their BG formation mechanisms. We demonstrate that the nonsymmorphic p4gm symmetry group design eminently surpasses the symmorphic p4mm-group design in both BG size and attenuation, achieving a wide 118% BG. This is possible by the coupling of the Bragg scattering and local resonance BG types in the p4gm design, absent in the classic p4mm Bragg BG. We numerically compute the BG for both p4mm and p4gm PnC designs and investigate how different designs and their corresponding mechanical properties influence BG formation mechanisms. We determine the type and attenuation performance of the BG by examining the vibration patterns and imaginary parts of the Bloch wave vectors, serving as quantifiable indicators of the waves' exponential decay. We conduct transmission loss simulations and experiments, for both P- and S-waves, to confirm the enhanced wave attenuation and wide BG achieved by coupling the two BG types, validating that transmission loss varies within the BG in agreement with the calculated evanescent modes.