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A model of piezoelectric phononic crystal (PC) double-layer nanobeam periodically attached by “spring-mass” resonators is proposed. As a comparison, two other simplified models are also proposed. In order to calculate the band structure, the plane wave expansion (PWE) method is improved by introducing the Euler beam and surface piezoelectricity theories. All the results and analysis demonstrate that the tunable advantage is displayed in double-layer nanobeam on account of the antisymmetric and symmetric vibrational modes controlled by adding additional springs between two different nanobeams. Moreover, the influencing rules of parameters related to additional spring and “spring-mas” resonator are also revealed. The bandgap properties can be applied to nano electro-mechanical system (NEMS) to realize active control of vibration.

Tunability of “spring-mass” resonator on band gaps with surface effects of a piezoelectric phononic crystal double-layer nanobeam