Features of the directional patterns of bulk elastic waves excited by a surface harmonic source in an anisotropic piezoelectric half-space

Abstract

On the basis of the stationary phase method and the saddle method in the proposed work, a numerical-analytical method was developed for constructing the asymptotics of elastic and electroelastic bulk waves, which are excited by a surface harmonic mechanical or electric delta source in a piezoelectric half-space. The anisotropy of elastic moduli, piezoelectric coefficients and dielectric constants can be arbitrary. An important element of the method is an algorithm for constructing the Fourier symbol of the Green's matrix of a piezoelectric half-space. Lithium niobate was chosen as a specific material for calculations. We calculated the directional patterns of the amplitudes of longitudinal and quasi-transverse waves in the symmetry plane of the Y-cut of lithium niobate, which are excited by three concentrated mechanical and electrical sources. For the plane of symmetry, six caustics of quasi-transverse waves were found, which are determined by degenerate stationary points. The range of ambiguity of asymptotic representations of quasi-transverse waves polarized in the plane of symmetry was found. The nature of ambiguity for bulk waves is similar to the analogous phenomenon for surface elastic waves in anisotropic media. In the absence of the piezoelectric effect, as well as in the case of a distributed source, the method does not require modification.