Seismic phononic crystals by elastodynamic Navier equation.

The phenomenon, known as a complete band gap in photonic crystals consisting of periodically arranged manmade nanostructures, caused a huge sensation in photonics. Inspired by the physical methodology, we extend it to large-scale wave propagation for seismic waves. In particular, we exploit the elastodynamic Navier equation in the medium for seismic phononic crystals to induce complete band gaps of body (P) and shear (S) waves. We also show a technique that uses weak formulation to analyze band structures. Estimation of evanescent modes by complex-valued wave vectors yields propagation length, then we redesign bulky phononic crystals to be as thin as possible. We also investigate how material properties affect the relation between propagation length and effective particle velocity. This study will contribute to seismic-resistant techniques in seismology.