Characterization of wave dispersion in viscoelastic cellular assemblies by doublet mechanics

Using the Voigt model, we analyze wave propagation in viscoelastic granular media with a monatomic lattice, planar simple cubic package and cubical - tetrahedral assembly within the context of doublet mechanics. Microstrains of elongation between the doublet particles are considered in the models. Wave dispersive relations are derived from dynamic equations of the particles involved in the media, and phase velocities and attenuations of the dispersive waves are obtained for the different assemblies. Variations in these dispersion characteristics are analyzed with the changes of cell interval, modulus, and wave frequency. The relations between micro-constants and macro-parameters are presented under the condition of non-scale continuity of the media.