Rayleigh and Bleustein–Gulyayev surface waves in elastic piezoelectric materials with relaxation of dielectric polarization

The non-linear equations describing models of elastic piezoelectric materials in an electromagnetic field, taking into account dielectric polarization relaxation processes, are considered. It is assumed that the relaxation is determined by the derivative of the Jaumann vector of the dielectric polarization. Linearization of the exact non-linear equations leads to a dependence of the dielectric polarization and the stress tensor on the rotation tensor of the deformation axes when there is a constant component of the dielectric polarization vector. Volume waves and Rayleigh and Bleustein–Gulyayev surface waves are considered, taking into account the relaxation of dielectric polarization in piezoelectric materials with axial symmetry. Dispersion equations are obtained, and the attenuation and logarithmic decrement of these waves are calculated. Dispersion of the wave velocity occurs when the relaxation of the dielectric polarization is taken into account. At low frequencies, the logarithmic decrements of the volume and surface waves are proportional to the square of the frequency. When the wave frequency increases, the logarithmic decrements approach constant finite values. It is shown, that the inclusion of the relaxation of the dielectric polarization when describing Rayleigh waves, reduces to simple replacement of the constant real coefficient in the Rayleigh equation in a complex parameters, the imaginary part of which is determined by the relaxation time.