Bandgap calculations of two-dimensional solid-fluid phononic crystals with the boundary element method

A boundary element method (BEM) is presented to compute the bandgaps of two-dimensional (2D) solid-fluid phononic crystals which are composed of square or triangular lattices with arbitrarily shaped scatterers. The system may be either an array of solid scatterers embedded in the fluid matrix or an array of fluid scatterers embedded in a solid matrix. The boundary integral equations of both matrix and scatterer are established for a periodic unit cell. Substituting the quasi-periodic boundary condition (i.e. Bloch-Floquet condition) and the interface conditions, an eigenvalue equation dependent on the Bloch wave vector is derived. The present method takes into account the solid-fluid interface conditions and the transverse wave mode in the solid component which has been proved to be significant. Some typical examples are illustrated to discuss the accuracy of the presented method and analyze the localization mode of the fluid scatterers. (c) 2012 Elsevier B.V. All rights reserved.