Band structure analysis of phononic crystals with imperfect interface layers by the BEM

Abstract

A boundary element method (BEM) is implemented and applied to compute the band structures of phononic crystals taking account of three different kinds of imperfect interface layers. By using the Bloch theorem and the interface conditions the eigenvalue equations related to the wave vector are derived. The influences of the spring-interface model, mass-interface model and spring-mass-interface model on the dispersion curves and the band-gaps are investigated by comparing with that of the perfect interfaces. For different interface models, the effects of various interface parameters and mass density ratios on the lower edge, upper edge and width of the first complete band-gap are analyzed and discussed. It will be shown that a weak interface imperfection would not affect the dispersion curves, but a relatively strong interface imperfection may significantly affect the band structures of phononic crystals and it cannot be ignored. Moreover, the three interface models have different influences on the wave propagation and band-gap characteristics of the phononic crystals.