Electric field, strain and inertia gradient effects on anti-plane wave propagation in piezoelectric materials

Abstract

In this study, we derive the dispersion relations for anti-plane waves in the second gradient electroelasticity theory considering the electric field, strain, and inertia gradient effects. Solutions are developed for bulk and surface shear horizontal (SH) waves including Bleustein–Gulyaev and Love waves. It is demonstrated that the presented model describes a normal dispersion of short waves in piezoelectric materials. The influence of additional model parameters (material characteristic length scales) on the phase velocity, coupled electromechanical factor, and attenuation of the SH waves is investigated. The non-classical upper bound for the Love wave velocity in the elastic layer/piezoelectric substrate system is given accounting for spatial dispersion. In the numerical examples, we use typical values of the length scale parameters of the order of the crystal lattice parameters such that all non-classical gradient effects are predicted for the electroelastic waves of the terahertz frequencies.