A BEM for band structure and elastic wave transmission analysis of 2D phononic crystals with different interface conditions. (August 2018) - Li, Feng-Lian
Highlights: A BEM is developed and applied for the band structure and elastic wave transmission analysis of 2D phononic crystals. A linear eigenvalue problem is formulated for the band structure computation of infinite phononic crystals. A linear system of algebraic equations is obtained for the elastic wave transmission computation in finite phononic crystals. The present BEM is verified by the DtN-map method. The effects of the interface boundary conditions between the matrix and the scatterers on the band structures and the elastic wave transmission of the phononic crystals are investigated by representative numerical examples. Abstract: In this paper, a boundary element method (BEM) is developed and applied to compute the band structures and the elastic wave transmission of 2D phononic crystals which have different interface conditions between the scatterers and the matrix. The 2D phononic crystals consist of circular or square solid cylinders periodically embedded in a solid matrix forming a square lattice. For a periodic unit-cell, the boundary integral equations for both the scatterer and the matrix are formulated. After discretizing the boundary integral equations and for an infinite periodic structure, a linear eigenvalue equation related to the Bloch wave vector is obtained by substituting the periodic boundary conditions and the interface conditions. While for the corresponding semi-infinite periodic structure, a linear equation set is obtained from which the elastic wave transmission can be obtained. To verify the present BEM, some representative numerical examples are presented for the phononic crystals with different acoustic impedance ratios. The numerical results indicate that the present BEM can efficiently provide accurate results for phononic crystals with arbitrary shapes and different interface conditions, and the interface conditions have important effects on the band structures and the elastic wave transmission. Graphical abstract: Image, graphical abstract