Designer band gaps in phononic crystals via nonsymmorphic symmetry

Phononic crystals (PnCs) are periodically-structured metamaterials designed to control the propagation of mechanical waves and have been used to create a multitude of acoustic devices. The increasingly-numerous uses of PnCs often require band gaps or pass bands within specific frequency intervals for various applications. The need for better control over the phononic band structure motivates this study from a crystallographic symmetry perspective. It is known from photonic and electronic theory that nonsymmorphic symmetry necessitates band-sticking within the band structure; this effect can simplify the process of controlling the band structure. This study numerically, and for the first time, experimentally investigates the effects of nonsymmorphic symmetry in 2D solid network PnCs with air inclusions. Band-sticking effects are evident in the computed band structures of nonsymmorphic PnCs, often resulting in less-dispersive bands and wider, multiple band gaps. Simulated results are in good agreement with experiments using ultrasonic transmission tests of glassy polymer PnC samples fabricated with stereolithographic printing. The experimental data show that these nonsymmorphic PnCs can achieve strong attenuation (by more than -70 dB relative to a solid reference of the same material) over multiple band gaps using a sample with only four layers of the basic unit cell.