Coiled Phononic Crystal with Periodic Rotational Locking: Subwavelength Bragg Band Gaps

Phononic crystals (PnC) are spatially periodic materials with band gaps that form by Bragg scattering of elastic waves. Within the frequency range a gap, wave propagation is not admitted. A long-standing limitation this class wavelength for band-gap formation must be on order unit-cell size. This restricts presence to relatively high frequencies given lattice spacing. Locally resonant metamaterials, other hand, enable opening low-frequency, subwavelength through resonance hybridization. However, their characteristically narrow and require large or massive local resonators form. Here, we break both limitations using beam-based PnCs (1) locking rotation degree freedom at edges primitive unit cell, (2) coiling PnC applying full beam-axis rotations locked locations. These respective kinematic geometric transformations convert conventional beam from its extended nominal constant an extremely compact coiled configuration greatly reduced constant. With rotational locking, remain intact still large, in fact increase noticeably subsequent coiling, based quantitatively conserved except now appearing lower as dictated ratio extended-to-coiled constants. defines factor, which measure reduction length direction transmission while maintaining structure original favorable changes induced locking. factor $\ensuremath{\beta}$ lowers, construction, location normalized central any gap $\ensuremath{\beta}$. The only need lateral space accommodate segments. vibration behavior finite version experimentally tested demonstrating matching response, despite length, obtained finite-element analysis rotationally version. concept creates effectively gaps. It clears path serve applications orders-of-magnitude smaller scale than currently possible, featuring significantly larger those generated locally metamaterials.