Electro-mechanical coupling band gaps of a piezoelectric phononic crystal Timoshenko nanobeam with surface effects

Plane wave expansion (PWE) method is extended to calculate the band structures of a proposed piezoelectric phononic crystal (PC) nanobeam by applying surface elasticity and Timoshenko beam theories. The calculation method is derived and formulized in detail. Further, electrical voltage and external axial force are picked to study the effects of electro-mechanical coupling fields on band gaps, residual surface stress and material intrinsic length are chosen to research the influences of surface effects on band gaps, and ratio between lengths of PZT-4 and epoxy in a unit cell and height-width ratio are picked to investigate the effects of geometric parameters on band gaps. In addition, all the results are compared to those in Euler nanobeam with same parameters. All the results and further analysis demonstrate that the influence rules will play an active role in design process and active control of nano electro-mechanical system based on piezoelectric PC nanobeam.