A local RBF collocation method for band structure computations of 2D solid/fluid and fluid/solid phononic crystals

In this paper, an efficient local radial basis function collocation method (LRBFCM) is presented for computing the band structures of the two-dimensional (2D) solid/fluid and fluid/solid phononic crystals. Both systems of solid scatterers embedded in a fluid matrix (solid/fluid phononic crystals) and fluid scatterers embedded in a solid matrix (fluid/solid phononic crystals) are investigated. The solid–fluid interactions are taken into account by properly formulating and treating the continuity/equilibrium conditions on the solid–fluid interfaces, which require an accurate computation of the normal derivatives of the displacements and the pressure on the fluid–solid interfaces and the unit-cell boundaries. The developed LRBFCM for the mixed wave propagation problems in 2D solid/fluid and fluid/solid phononic crystals is validated by the corresponding results obtained by the finite element method (FEM). To the best knowledge of the authors, the present LRBFCM has yet not been applied to the band structure computations of 2D solid/fluid and fluid/solid phononic crystals. For different lattice forms, scatterers' shapes, acoustic impedance ratios, and material combinations (solid scatterers in fluid matrix or fluid scatterers in solid matrix), numerical results are presented and discussed to reveal the efficiency and the accuracy of the developed LRBFCM for calculating the band structures of 2D solid/fluid and fluid/solid phononic crystals. A comparison of the present numerical results with that of the FEM shows that the present LRBFCM is much more efficient than the FEM for the band structure computations of the considered 2D solid/fluid and fluid/solid phononic crystals. Copyright © 2016 John Wiley & Sons, Ltd.