A Distributed-Parameter Flexoelectric Energy Harvester Model Accounting for Two-Way Coupling and Size Effects

We present a distributed-parameter electromechanical model and its modal analysis for flexoelectric energy harvesting using centrosymmetric dielectrics by accounting for both the direct and converse effects as well as size dependence of the coupling coefficient. Flexoelectricity is the generation of electric polarization in elastic dielectrics by the application of a non-uniform mechanical strain field, i.e. a strain gradient. In order to accompany atomistic simulations and experimental efforts at small scales, there is a growing need for high-fidelity device models that can also provide an analytical insight into size-dependent electro-elastodynamics of small structures that exhibit and exploit flexoelectricity. Particularly, although the conversion of mechanical energy into electrical energy (i.e. energy harvesting) is more related to the direct effect, it is necessary to accurately model the converse effect for thermodynamic consistency and completeness. To this end, we present a flexoelectric monolayer centrosymmetric energy harvester model (that yields no piezoelectric effect) for converting ambient vibration into electricity. The flexoelectric energy harvester model based on the Euler-Bernoulli beam theory is focused on strain gradient-induced polarization resulting from the bending (transverse) vibration modes in response to mechanical base excitation. Following recent efforts on the converse flexoelectric effect in finite samples, the proposed model accounts for two-way coupling, i.e. the direct and converse effects, and it also captures the effect of geometric scaling on the coupling coefficient. In addition to closed-form solutions of the electromechanical frequency response functions, various case studies are presented for a broad range of material and geometric parameters. Thickness dependence of the electromechanical coupling is analytically shown and is observed in simulations of the electromechanical frequency response functions as well.