Size-dependent vibrations and waves in piezoelectric nanostructures:a literature review

With the development and applications of nano-electro-mechanical systems,academic interest in the mechanical behavior of piezo-electric structures at nanoscale is increasing.Interesting unconven-tional phenomena have been observed either experimentally or through molecular dynamics simulation.The most common and also important one is the size-dependent characteristics.Classical continuum mechanics with necessary modifications has been pro-ven to be very powerful in explaining these particular characteris-tics in a relatively simple theoretical framework.This article reviews the recent advances in understanding the size-dependent dynamic responses of piezoelectric nanostructures from the viewpoint of modified continuum mechanics.Particular attentions are paid to three advanced theories of piezoelectricity(e.g.gradient piezoelec-tricity,surface piezoelectricity,and nonlocal piezoelectricity)and their abilities to predict unconventional vibration and wave char-acteristics in piezoelectric structures and devices at the nanoscale.The article could serve as a useful reference for the future research on or design of nanostructures with multifield couplings.