Flexoelectric and transverse shear effects on band gaps in periodic microbeams

This paper applies wave equations and boundary conditions to a periodic electro-elastic microbeam, which incorporates transverse shear, microstructure and flexoelectric effects to anticipate the occurrence of band gaps in elastic waves. The new model has been simplified as the flexoelectric model and classical elastic model, as special cases. Meanwhile, compared to Bernoulli-Euler beam model, it is found that transverse shear effect has a significant effect on the band gap predictions of thick beams, but this effect is negligible for slender beams, indicating that this new model can be used to predict band gaps of both thick and slender beams in the high-frequency range. Furthermore, the impacts of microstructure and flexoelectric effects as well as material and microstructural parameters on band gaps are studied. The numerical results show that the influence of flexoelectricity on band gaps is the primary in the submicron beams, while the microstructure effect is the main in the micron beams. Additionally, the band gap frequencies and sizes (bandwidth) are significantly affected by the beam thickness, unit cell length and volume fraction. Thus, these discoveries demonstrate the feasibility of tailoring the band gap frequencies and sizes through the adjustment of material and microstructural parameters.