1D Elastic Metamaterial · Bragg Scattering · Band Structure
Crystal Parameters
Transfer Matrix
M = M₁ · M₂ · M₁ · ...
cos(ka) = ½Tr(M)
Bandgap: |½Tr(M)| > 1
Computing band structure...
Physics
Phononic crystals are periodic elastic media where Bragg scattering at layer interfaces opens frequency gaps. Waves in the bandgap decay exponentially (evanescent modes). The transfer matrix method gives exact band structure for 1D systems. Contrast in acoustic impedance Z=√(ρE) determines gap width.