Pure modes for elastic waves in crystals: mathematical modeling and search

A universal search method of pure longitudinal and pure transverse modes for elastic wave propagation in crystals, in general piezoelectrics, is presented. A mathematical model of pure modes for elastic waves based on adiabatic state equations for an arbitrary anisotropic piezoelectric medium and its equation of motion under elastic deformations in the rotated Cartesian coordinates is constructed. The condition for longitudinal normals is that all non-diagonal matrix elements of the effective elastic stiffness coefficients in the corresponding wave equation are equal to zero. Equating to zero non-diagonal elements only in one row of this matrix, one can obtain the condition for transverse normals. A computer program is prepared which allows to find the pure modes for elastic waves in crystals and to calculate their characteristics when symmetry class, elastic, piezoelectric, dielectric constants, and crystal density are known.