Vibrating piezoelectric nanofilms as sandwich nanoplates

Abstract

Vibrating piezoelectric nanofilms (PNFs) play an important role in developing electromechanical nanodevices. To accurately characterize their dynamic behavior a sandwich-plate model is developed by integrating the surface effect and piezoelectric effect into the elastic plate theory. It is then used to analyze the vibration of PNFs with an emphasis on the effect of piezoelectricity and the surface layers. Analytic formulae are derived to identify the key factors that determine the structural responses of PNFs. Their influence on the vibration of PNFs is then evaluated qualitatively in a numerical study. It is found that the surface effect is significant and originates primarily from the residual surface stresses and the equivalent pre-stresses induced by an electrical voltage via the surface piezoelectricity.