Micro-structural effects in phononic dielectric structures

Abstract

Based on the higher-grade continuum theory, propagation of longitudinal as well as transverse anti-plane elastic waves in normal direction to nanoscale periodic laminates of piezoelectric dielectrics is studied in this paper. The strain gradients, micro-inertia and direct flexoelectricity phenomena are incorporated into the phenomenological description. The problem is analysed as one-dimensional and the governing equations together with possible boundary conditions are derived from the Hamilton variation principle. It is shown that the transverse waves are not affected by the electric polarization in contrast to the longitudinal waves. The developed formulation is applied to 1D Bloch waves obeying perfect boundary conditions periodical in bi-material laminates and the transfer matrix method is used for derivation of dispersion equation. An analytical method is developed for solution of the dispersion equation. The influence of the micro-stiffness and micro-inertial length scale parameters as well as flexoelectric coefficients on the dispersion curves and the frequency gaps is investigated in parametric study.