The paper describes a mathematical model of plane wave propagation in elastic and piezoelectric layered phononic crystals with a finite number of unit-cells. Wave motion is excited by an incident plane P- or SV- wave coming from an outer elastic half-space. The wavefield is obtained by using the transfer matrix (T-matrix) method. The methods to construct a T-matrix of a piezoelectric layer and T-matrix of the periodic structure consisted of given number of unit-cells are developed. The transmitted wave field is expressed in terms of expansion in eigenvalues of the T-matrix unit-cell. A classification of band-gaps and pass-bands in layered phononic crystals is proposed. The classification relies on the analysis of the eigenvalues of T-matrix for a unit-cell and the asymptotics for the transmission coefficient, when the number of the unit cells tends to infinity. Two kinds of band-gaps, where the transmission coefficient decays exponentially with the number of unit-cells, are specified. The so-called low transmission pass-bands (LTPB) are introduced in order to identify frequency ranges where the wave transmission is very low, but it does not tend to zero exponentially. Very week conversion effects of modes are observed in the LTPB. The types of band-gaps and their transformation with a change of the incident angles are discussed with numerical examples. The influence of piezoelectric and dielectric constants on width and location of band-gaps is studied.

Исследуется распространение упругих волн в периодическом композите, составленном из пьезоэлектроупругих слоев. Колебания генерируются падающей плоской P- или SV-волной. Волновые поля строятся с использованием метода матриц переноса. Анализируется влияние частоты колебаний, угла падения и типа падающей волны. Исследуется влияние материальных свойств пьезоэлектрических слоев ячейки на распространение и фильтрацию упругих волн в фононных кристаллах.