Bandgap and its defect band analysis of flexoelectric effect in phononic crystal plates.

The wave equations of a novel model for the electro-elastic Kirchhoff plate containing the flexoelectric effect are constructed using a variational formulation. Through an Improved Plane Wave Expansion (IPWE) approach, the proposed wave equations are then applied to examine the elastic wave bandgap and defect band in a phononic crystal plate structure without or with a defect. The results demonstrate that the flexoelectric effect on the bandgap is apparent when the structure is at the submicron scale and fades as the scale increases. Moreover, at all length scales, the magnitude of the bandgap varies dramatically with lattice length and inclusion volume ratio. This suggests that the frequency and broadness of the bandgap can be tuned by modifying the volume percentage of inclusion, plate size parameters and lattice length. The dispersion curves of the defect model and corresponding mode shape at the defect band are also studied, which can indicate the applicability of the current model incorporating flexoelectric effect in energy harvesting and wave focusing. The novel model and these findings would help the design of MEMS/NEMS devices for enhanced wave guiding when flexoelectric-based electro-elastic fields are involved. • Wave equations of a novel model for the electro-elastic Kirchhoff plate with flexoelectric effect are proposed. • The bandgap and defect band in a phononic crystal plate are analytically solved based on the new wave equations. • The flexoelectric effect is apparent when the plate is at the submicron scale and fades as the scale increases. • The dispersion curves of the defect model and corresponding mode shape at the defect band can be obtained. • The novel model and numerical results are useful for enhancing energy harvesting and wave focusing. [ABSTRACT FROM AUTHOR]