Mathematical modeling of the propagation of electroacoustic shear waves in a layered periodic medium “Piezoelectric - gap”

The paper developed a method for constructing dispersion relations for bulk, surface and normal electroelastic shear waves propagating in layered-periodic media formed by repeating a "generating" package consisting of a piezoelectric layer and a vacuum layer that does not have electrical properties. As a result of the analytical calculations, dispersion relations for surface, normal and bulk electroelastic shear waves were obtained. CdS was considered as a piezoelectric material. The obtained dispersion relations were numerically analyzed for different layer geometries and physical properties of materials forming the "generating" package. . Numerical analysis showed that a feature of the obtained bulk wave spectrum is that in the range of changes in the wave number and circular frequency, the zone boundaries do not intersect. The spectrum of normal waves is formed by a set of dispersion curves, which is localized in the zones of transmission of bulk waves except for one dispersion curve from the set. This curve is a dispersion curve for surface modes. The set of dispersion curves of normal modes consists of n curves (n is the number of electroelastic "generating" packages in the structure). The influence of the physical-mechanical and geometric parameters of the layers on the structure of the blocking and transmission zones has been studied, and the influence of the piezoelectric effect has also been investigated.Based on the approaches proposed in previous works, the problems of bulk, surface and normal electroelastic waves are reduced to the study of the properties of the transmission matrices of the "generating" package of layers, through the elements of which the desired dispersion relations are expressed. In the work, it was possible, using the condition of metallization on the outer surfaces of the package, to write the dispersion relations through the elements of the second-order matrices instead of the fourth, which made it possible to simplify the analysis of the dispersion equations.