Tuning of 2D Phononic Band Structures via Buckling Instability

Dispersion relation of propagating elastic waves through phononic crystals, which are periodic elastic structures, can be represented with band diagrams akin to the electronic band structures and band structures in photonic crystals. Of special interest in these diagrams are band gaps, which correspond to frequencies of waves that cannot be transmitted through the bulk of the phononic crystals. The location of band gaps depends on the material properties and on the geometry and symmetries of phononic structures. The symmetries of compressed elastic structures can be drastically altered via the buckling instability, and we are exploring how that affects the phononic band structures. First, we systematically investigated band diagrams for uncompressed 2D phononic structures that belong to different crystallographic groups. We employed recently developed tools for electronic systems, to analyze which band crossings are topologically protected/prohibited. We use this information to analyze how band structures are affected by the buckling instability, which causes a phononic structure to move from one crystallographic group to another. Such tuning of band structures with external load could then be used to engineer tunable sound filters as well as mechanical sensors.