Electro-mechanical coupling properties of band gaps in an with periodically attached “spring-mass” resonators

The model of a locally resonant (LR) epoxy/PZT-4 phononic crystal (PC)nanobeam with “spring-mass” resonators periodically attached to epoxy is proposed. The corresponding band structures are calculated by coupling Euler beam theory, nonlocal piezoelectricity theory and plane wave expansion (PWE) method. Three complete band gaps with the widest total width less than 10GHz can be formed in the proposed nanobeam by comprehensively comparing the band structures of three kinds of LR PC nanobeams with resonators attached or not. Furthermore, influencing rules of the coupling fields between electricity and mechanics,“spring-mass” resonator, nonlocal effect and different geometric parameters on the first three band gaps are discussed and summarized. All the investigations are expected to be applied to realize the active control of vibration in the region of ultrahigh frequency.