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.     

Dispersion Analysis of Wave Propagation in Cubic-Tetrahedral Assembly by Doublet Mechanics

Based on elongation and shear microstrains between the doublet particles, we present the dynamic scaling equations of plane wave propagation in a cubic-tetrahedral assembly (lattice type H4) in accordance with the formalism of doublet mechanics (DM). The relations between the micro-moduli of DM constitutions and the macroparameters of the Cosserat continuum model are obtained by a mapping process and a non-scale approximation of the DM model. With multi-scale characteristics, the frequency dispersion curves from DM reflect the effect of granule inhomogeneity and the anisotropic nature of the micro-structure on the wave propagation in the H4 medium.     

Spectral Problems for the Orientation—Free Discrete Kinetic Models

We present computations using orientation-free discrete velocity models for the dispersion relationship of ultrasound propagation in monatomic hard-sphere gases (or a type of gas composed of a system of vortices).Comparisons with previous verified fixed-orientation results for the propagation of the sound mode in rarefied gases show that,if collective excitations are considered,an orientation-free eight-velocity model can capture more physical insights.We also demonstrate the symmetry property of the spectra using the orientation-free eight-velocity model.