Abstract This paper investigates the bandgap properties of a piezoelectric periodic nano-beam considering size and surface effects using a modified couple stress theory. The nano-beam is made of some finite periodic arrays of piezoelectric (PZT-5H) and epoxy segments. The Bloch theorem for periodic materials together with the transfer matrix method are employed for analyzing the problem. The band structures analyzed by the current model incorporates both the material length scale parameter and surface effects in the bulk and surface layer of the beam, respectively. The main objective of this study is to investigate the effects of different parameters such as external electrical loading, length scale parameter, surface effects and geometrical properties of the nano-beam on the width of bandgaps and the starting frequencies. It is found that when the external electrical field is increased, the surface effects on the bandgaps are increased. Also, for high values of length to height ratio, the surface effects reduce the number of bandgaps. The results of the current study may be helpful in designing piezoelectric periodic nano sensing devices.

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