Size-dependent dynamics of flexoelectric and flexoelectric-piezoelectric structures

Abstract

Flexoelectricity is the generation of electric polarization by the application of a non-uniform mechanical strain field, i.e. a strain gradient. Unlike piezoelectricity (strain-induced polarization), flexoelectric coupling is associated with a fourth rank tensor, and is exhibited by all elastic dielectrics regardless of the material symmetry; however, as a gradient effect, flexoelectricity is expected to be significant only at very small scales. This work aims to develop electromechanical models to analyze the dynamics and vibration of structures leveraging flexoelectricity and to establish analytical and approximate analytical frameworks for next-generation submicron concepts and devices for energy harvesting, sensing, and actuation. At such small geometric scales, flexoelectricity yields electromechanical behavior even in non-piezoelectric dielectric materials, while it enhances the electromechanical coupling in piezoelectric ones. In particular, energy harvesting is a potential future application area of flexoelectricity to enable ultra-low-power nanoscale devices by converting vibrations into electricity. The focus of this work is first placed on bending vibrations of centrosymmetric cantilevers, such as a monolayer STO (Strontium Titanate) cantilever. An electroelastodynamic framework is presented and analyzed for flexoelectric power generation from strain gradient fluctuations in centrosymmetric dielectrics, by accounting for the presence of a finite electrical load across the surface electrodes as well as two-way electromechanical coupling, and capturing the size effect. In addition to the electromechanical frequency response functions, the transverse mode flexoelectric coupling coefficient is obtained analytically; its dependence on the cantilever thickness and a material figure of merit is shown. The modeling framework is then extended to non-centrosymmetric configurations, such as bimorph cantilevers made from Barium Titanate (BTO), to understand and quantify the interaction between flexoelectricity and piezoelectricity for different thickness levels. The effects of varying cross section are also of interest, requiring the use of approximate analytical electromechanical modeling frameworks. Geometrically nonlinear frameworks for flexoelectric and flexoelectric-piezoelectric configurations, as well as linear two-dimensional plate frameworks, are also developed and case studies are presented for different geometric scales. Other than bending vibrations leveraging the transverse mode, this work includes the leveraging of axial vibrations to develop a framework for the dynamics and vibration of truncated nanostructures in thickness mode.