Flexoelectricity, representing a spontaneous electric polarization induced by a non-uniform strain field (or strain gradient), is believed to become manifest and be responsible for the size-dependent properties of dielectric materials at the nanoscale. In this paper, the influence of the flexoelectric effect on the static bending and free vibration of a simply supported piezoelectric nanobeam is investigated based on the extended linear piezoelectricity theory and the Timoshenko beam model. The governing equations of the piezoelectric nanobeam with non-homogeneous boundary conditions are obtained from Hamilton's principle. Explicit expressions of the beam deflection and resonant frequency are derived to show the size-dependency of the flexoelectric effect. It is found that the flexoelectricity has a significant effect on the deflection of the bending beam and may reverse the deflection direction under certain loading conditions. Simulation results also indicate that the influence of the flexoelectricity on the vibration behaviour of the piezoelectric nanobeam is more prominent for beams with smaller thickness. Thus, it is suggested that possible frequency tuning of piezoelectric nanobeams by adjusting the applied electrical load should incorporate the flexoelectric effect. The current study can be claimed as helpful for qualitatively characterizing the trend of the flexoelectric effect on the mechanical responses of piezoelectric nanobeams.

This work investigates the surface effects on the vibration and buckling behaviour of a simply supported piezoelectric nanoplate (PNP) by using a modified Kirchhoff plate model. Two kinds of in-plane constraints are defined for the PNP, and the surface effects are accounted in the modified plate theory through the surface piezoelectricity model and the generalized Young–Laplace equations. Simulation results show that the influence of surface effects on the plate resonant frequency depends on the in-plane constraints significantly. For the PNP with different in-plane constraints, the effects of the applied electric potential, the mode number, the plate aspect ratio and the plate thickness on the resonant frequency are examined with consideration of the surface effects. The possible mechanical buckling of the PNP is also studied, and it is found that the surface effects on the critical electric voltage for buckling are sensitive to the plate thickness and aspect ratio. Our results also reveal that there exists a critical transition point at which the combined surface effects on the critical electric voltage may vanish under certain conditions.

Piezoelectric nanomaterials (PNs) are attractive for applications including sensing, actuating, energy harvesting, among others in nano-electro-mechanical-systems (NEMS) because of their excellent electromechanical coupling, mechanical and physical properties. However, the properties of PNs do not coincide with their bulk counterparts and depend on the particular size. A large amount of efforts have been devoted to studying the size-dependent properties of PNs by using experimental characterization, atomistic simulation and continuum mechanics modeling with the consideration of the scale features of the nanomaterials. This paper reviews the recent progresses and achievements in the research on the continuum mechanics modeling of the size-dependent mechanical and physical properties of PNs. We start from the fundamentals of the modified continuum mechanics models for PNs, including the theories of surface piezoelectricity, flexoelectricity and non-local piezoelectricity, with the introduction of the modified piezoelectric beam and plate models particularly for nanostructured piezoelectric materials with certain configurations. Then, we give a review on the investigation of the size-dependent properties of PNs by using the modified continuum mechanics models, such as the electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics. Finally, analytical modeling and analysis of nanoscale actuators and energy harvesters based on piezoelectric nanostructures are presented.

Dielectric elastomer generators (DEGs), as a recent transduction technology, harvest electrical energy by scavenging mechanical energy from diverse sources. Their performance is affected by various material properties and failure modes of the dielectric elastomers. This work presents a theoretical analysis on the performance of a dielectric elastomer membrane generator under equi-biaxial loading conditions. By comparing our simulation results with the experimental observations existing in the literature, this work considers the fatigue life of DE-based devices under cyclic loading for the first time. From the simulation results, it is concluded that the efficiency of the DEG can be improved by raising the deforming rate and the prescribed maximum stretch ratio, and applying an appropriate bias voltage. However, the fatigue life expectancy compromises the efficiency improvement of the DEG. With the consideration of the fatigue life, applying an appropriate bias voltage appears to be a more desirable way to improve the DEG performance. The general framework developed in this work is expected to provide an increased understanding on the energy harvesting mechanisms of the DEGs and benefit their optimal design.