Abstract
A wavelet-based boundary element method is employed to calculate the band structures of two-dimensional phononic crystals, which are composed of square or triangular lattices with scatterers of arbitrary cross sections. With the aid of structural periodicity, the boundary integral equations of both the scatterer and the matrix are discretized in a unit cell. To make the curve boundary compatible, the second-order scaling functions of the B-spline wavelet on the interval are used to approximate the geometric boundaries, while the boundary variables are interpolated by scaling functions of arbitrary order. For any given angular frequency, an effective technique is given to yield matrix values related to the boundary shape. Thereafter, combining the periodic boundary conditions and interface conditions, linear eigenvalue equations related to the Bloch wave vector are developed. Typical numerical examples illustrate the superior performance of the proposed method by comparing with the conventional BEM.
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