Band-gaps and low transmission pass-bands in layered piezoelectric phononic crystals

In-plane wave propagation in layered piezoelectric phononic crystals composed of functionally graded interlayers arisen from the solid diffusion is considered in the present work. Wave transmission and band-gaps due to the material gradation and incident wave-field are investigated. A classification of band-gaps in layered piezoelectric functionally graded phononic crystals is proposed. The classification relies on the analysis of the eigenvalues of the transfer matrix for a unit-cell and the asymptotics derived for the transmission coefficient. The so-called low transmission pass-bands are introduced in order to identify frequency ranges, in which the wave transmission is sufficiently low for engineering applications, but it does not tend to zero exponentially as the number of the unit-cells tends to infinity. Wave-fields, low transmission pass-bands and band-gaps in layered and functionally graded piezoelectric phononic crystals are analyzed.