Band gaps of elastic waves in 1-D dielectric phononic crystal with the flexoelectric and strain gradient effects consideration

The propagation of Bloch waves in one dimensional phononic crystal consisting of dielectric elastic solids is studied with consideration of the strain gradient, inertial gradient and flexoelectric effects. The transfer matrixes for single layer and one-cell of phononic structure are derived based on the constitutive equations and the governing equations of dielectric elastic solids. The dispersion equation for Bloch waves is obtained by the application of periodic conditions for the generalized displacements and tractions considered within strain gradient theory of electro-elasticity. Based on the numerical solution of the derived dispersion equation, the influences of the micro-stiffness length scale, micro-inertial length scale and flexoelectric coefficients on the dispersion and the bandgap are discussed.