Transmission and resonances in layered phononic crystals with damages

Elastic wave propagation in layered non-damaged and damaged phononic crystals is investigated using the extended transfer matrix method, the boundary integral equation method and the spring boundary conditions. Two different models are developed to approximate the layer with a distribution of damages, namely, a periodic array of cracks and continuously distributed springs in the layer. The focus of this analysis is on the wave transmission and reflection, band-gaps, localization and resonance phenomena due to crack-like damages.