Abstract
This paper describes a mathematical model of plane wave propagation in anisotropic and functionally graded layered phononic crystals with finite and infinite number of unit-cells. Classification of pass-bands and band-gaps is presented based on asymptotic analysis of the wave-fields in periodic layered structures. Two kinds of band-gaps where the transmission coefficient decays exponentially with the number of unit-cells are specified. The so-called low transmission pass-bands are introduced in order to identify frequency ranges in which the transmission is low enough for engineering applications, but it does not tend to zero exponentially with the number of unit-cells approaching infinity. The results of the numerical simulation are presented in order to demonstrate wave propagation phenomena. The influence of the anisotropy and functionally graded interlayers on the band-gaps and pass-bands is analysed.
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