Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a spring-mass resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.