Application of the 2D Models of Media with Dense and Non-dense Packing of the Particles for Solving the Parametric Identification Problems

Theoretical estimates [1] and experimental data [2, 3, 4, 5] show that rotational waves can exist in solids in the high-frequency field (> 109 – 1011 Hz), where it is rather difficult to carry out acoustic experiments with the technical viewpoint. The question arises: is it possible to obtain some information about the microstructure of a medium from acoustic measurements in the low-frequency range (106 – 107 Hz), when the rotational waves do not propagate in the medium? To this purpose, we will consider in this chapter the low-frequency approximation of Eqs. (2.8) and (3.6), in which the microrotations of the particles of the medium are not independent and are determined by the displacement field. Further, by comparing the obtained equations describing the propagation and interaction of longitudinal and transverse waves in a granular medium in the low-frequency approximation with the equations of the classical theory of elasticity, we will consider the problem of parametric identification of the developed models.