Using an extension of the full elastodynamic layer-multiple-scattering method to structures of fluid-saturated poroelastic spherical bodies, a comprehensive theoretical study of the acoustic response of double-porosity submerged liquid-saturated granular polymeric materials of specific morphology consisting of touching porous polymer spheres arranged in a fcc lattice, beyond the long-wavelength effective-medium description, is presented. Calculated transmission and absorption spectra of finite slabs of these materials are analyzed by reference to the acoustic modes of the constituent porous spherical grains as well as to relevant dispersion diagrams of corresponding infinite crystals, and a consistent interpretation of the results is provided. In particular, it is shown that resonant modes with very long lifetime, localized in the spheres in the form of slow longitudinal waves, which are peculiar to poroelastic materials, are formed when the viscous length is much shorter than the radius of the inner pores of the spheres. These modes, which can be easily tuned in frequency by adjusting the intrinsic porosity of the spheres, induce some remarkable features in the acoustic behavior of these double-porosity materials, such as narrow dispersionless absorption bands and directional transmission gaps.
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