Lamb wave propagation with flexoelectricity and strain gradient elasticity considered

Abstract

In this paper, the effects of flexoelectricity and strain gradient elasticity on Lamb waves propagating in an infinite piezoelectric nanoplate are analytically investigated. The dispersion equations are obtained and numerically solved for both the electrically open and short cases. A detailed discussion about the dispersion relations of the lowest mode is subsequently presented. Numerical results indicate that flexoelectricity and strain gradient elasticity have a substantial effect on Lamb wave propagation. Compared with the phase velocity of classical piezoelectric Lamb waves, flexoelectricity could decrease the phase velocity, while strain gradient elasticity could increase it. The effects of flexoelectricity and strain gradient elasticity largely depend on the wave number, material properties and nanoplate thickness. In infinite PZT-5H ceramic nanoplates, the effects of flexoelectricity and strain gradient elasticity on the phase velocity are negligible for wave numbers less than 106 m−1. However, for larger wave numbers, not only the phase velocity but also the dispersion relations can be significantly changed with the introduction of flexoelectricity and strain gradient elasticity. In addition, the effects of flexoelectricity and strain gradient elasticity on the electromechanical coupling coefficient are significant and complicated. Since the flexoelectric effect and the strain gradient elasticity effect exist in almost all dielectric materials, the conclusions obtained in this paper are general and can be applied to the analysis and design of the acoustic devices based on Lamb wave propagation.