Abstract:
The relevance of the research is determined by the need to simulate wave propagation in
heterogeneous media based on phononic crystals. These studies are necessary for the tasks of flaw
detection, the development of non-destructive testing methods, geophysics, engineering geophysics
and other methods of acoustic research. During the study, it was determined that the fragmentation
of the components of two-component phononic crystals into 2, 3, . . . N equal parts in the unit
cell leads to a catastrophic rearrangement of the dispersion relations and the appearance of new
elementary wave packets for acoustic waves. Using numerical-analytical methods, it is shown that in
two-component phononic crystals, the polydispersity of the components can significantly affect the
average characteristics of the propagation of long acoustic waves when the polydisperse crystal is
close to monodisperse with a smaller unit cell size. For polydisperse crystals close to monodisperse
with the same period (unit cell size), their averaged characteristics for long waves coincide.
