  We analyse the propagation of pressure waves within a fluid filled with a
three-dimensional array of rigid coated spheres (shells). We first draw band
diagrams for corresponding Floquet-Bloch waves. We then dig a channel
terminated by a cavity within each rigid shell and observe the appearance of a
low frequency stop band. The underlying mechanism is that each holey shell now
acts as a Helmholtz resonator supporting a low frequency localized mode: Upon
resonance, pressure waves propagate with fast oscillations in the thin water
channel drilled in each shell and are localized in each fluid filled inner
cavity. The array of fluid filled shells is approximated by a simple mechanical
model of springs and masses allowing for asymptotic estimates of the low
frequency stop band. We finally propose a realistic design of periodic
macrocell with a large defect surrounded by 26 resonators connected by thin
straight rigid wires, which supports a localized mode in the low frequency stop
band.
