Features of the Propagation of Long Waves in Phononic Crystals, the Influence of the Concentration and Polydispersity of the Components

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.