  The paper describes a novel methodology of designing granular phononic
crystals for acoustic wave manipulations. A discrete element method is utilized
to model the dynamics of a pulse wave propagating through the densely packed
assembly of elastic spherical particles with an embedded phononic crystal - the
region consisting of a certain arrangement of particles with varying densities.
We suggest an optimization strategy that extremizes the useful properties of a
granular phononic crystal, which are described in terms of a noise-proof
functional based on frequency-wavenumber summation of spectral energy density.
Few types of efficient phononic crystals are identified. The suggested
methodology is of interest for a number of applications, in particular, for
seismic shielding and selective sound absorption.
