The Advanced Boundary Integral Equation Method for Modelling Wave Propagation in Layered Acoustic Metamaterials with Arrays of Crack-Like Inhomogeneities

Abstract

The three-dimensional problem of the modelling of elastic wave propagation in a multi-layered acoustic metamaterial, a periodic elastic composite with periodic arrays of interface cracks or planar voids of arbitrary shape, is considered. The boundary integral equation method is extended for this purpose. The unknown crack-opening displacement vectors for each array are related using the Floquet theorem and solved using the Galerkin method at reference delaminations in the arrays. The developed method provides an efficient tool for fast parametric analysis of the influence of the periodic crack array characteristics on the transmission and diffraction of elastic waves. Two modifications to the boundary integral equation method are proposed and compared for rectangular cracks. To reduce computational costs, a preliminary analytical evaluation of the arising integral representations in terms of the Fourier transform of Green’s matrices and the crack-opening displacements are presented.

Keywords

• wave propagation
• boundary integral equation method
• spectral method
• acoustic metamaterial
• crack
• void