DISPERSION RELATIONS OF A PERIODIC ARRAY OF FLUID-FILLED HOLES EMBEDDED IN AN ELASTIC SOLID

Abstract

Dispersive properties of elastic waves in a periodic composite with an array of fluid-filled holes are studied in this paper. A finite element method taking into account of the fluid–solid interaction is developed to calculate the dispersion curves. The finite element formulation is presented for one unit cell by taking advantage of the periodicity of the structures and the Bloch theorem. After dividing the equations in the real and imaginary parts, the numerical computation is performed by using the standard finite element code ABAQUS. As numerical examples, some typical two- and three-dimensional systems with circular or spherical holes filled with air, water or mercury are considered in detail. The method can yield precise results with fast convergence for all cases from very low-density fluids to very high-density fluids.