Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory

We report on nanoscale strain gradients in ferroelectric HoMnO3 epitaxial thin films, resulting in a giant flexoelectric effect. Using grazing-incidence in-plane x-ray diffraction, we measured strain gradients in the films, which were 6 or 7 orders of magnitude larger than typical values reported for bulk oxides. The combination of transmission electron microscopy, electrical measurements, and electrostatic calculations showed that flexoelectricity provides a means of tuning the physical properties of ferroelectric epitaxial thin films, such as domain configurations and hysteresis curves.

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Giant Flexoelectric Effect in Ferroelectric Epitaxial Thin Films

In this work, the influence of surface effects, including residual surface stress, surface elasticity and surface piezoelectricity, on the vibrational and buckling behaviors of piezoelectric nanobeams is investigated by using the Euler-Bernoulli beam theory. The surface effects are incorporated by applying the surface piezoelectricity model and the generalized Young-Laplace equations. The results demonstrate that surface effects play a significant role in predicting these behaviors. It is found that the influence of the residual surface stress and the surface piezoelectricity on the resonant frequencies and the critical electric potential for buckling is more prominent than the surface elasticity. The nanobeam boundary conditions are also found to influence the surface effects on these parameters. This study also shows that the resonant frequencies can be tuned by adjusting the applied electrical load. The present study is envisaged to provide useful insights for the design and applications of piezoelectric-beam-based nanodevices.

https://iopscience.iop.org/article/10.1088/0957-4484/22/24/245703/pdf

The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects

Flexoelectricity in solids: Progress, challenges, and perspectives

Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory

In this work, surface effects, including surface elasticity, residual surface stress and surface piezoelectricity, are considered to study the electromechanical coupling (EMC) behaviour of piezoelectric nanowires (NWs) with the Euler–Bernoulli beam theory. Using the surface-layer-based model, explicit formula for EMC coefficient is derived. It is clearly observed that this coefficient is size-dependent and can be strongly enhanced when the geometric dimensions of NWs scale down. The static bending of a cantilever piezoelectric NW is also studied. The surface effects are found to significantly influence the stiffness and electric field distribution in the NW. The results indicate that surface effects play a significant role in the EMC and bending behaviours of piezoelectric nanobeam. This work is very helpful for understanding the size-dependent properties of nanostructured piezoelectric materials and improving the performance of the piezoelectric nanobeam-based devices in energy harvesting.

http://iopscience.iop.org/article/10.1088/0022-3727/44/7/075404/pdf

Surface effects on the electromechanical coupling and bending behaviours of piezoelectric nanowires

Flexoelectricity, referring to a spontaneous electric polarization induced by strain gradient in dielectrics, presents a strong size dependency at the nanoscale. In the current work, the influence of the flexoelectric effect on the mechanical and electrical properties of bending piezoelectric nanobeams with different boundary conditions is investigated. Based on the extended linear piezoelectricity theory and the Euler beam model, analytical solutions of the electroelastic fields in the piezoelectric nanobeams subjected to both electrical and mechanical loads are obtained with the inclusion of the flexoelectric effect. Simulation results show that the flexoelectric effect on the elastic behavior of bending beams is sensitive to the beam boundary conditions and the applied electrical load. In addition, for a cantilever piezoelectric nanobeam, an axial relaxation strain is induced from the piezoelectric and flexoelectric effects, while these effects induce a resultant axial force in both the clamped-clamped and simply supported piezoelectric nanobeams. Results also indicate that the flexoelectric effect plays a significant role in the contact stiffness and electric polarization of piezoelectric beams when their thickness is at the nanoscale. It is found that the flexoelectric effect on the electroelastic responses of piezoelectric nanobeams is more pronounced for the beams with smaller thickness. These results are useful for understanding the fundamental mechanical and physical properties of bending piezoelectric nanobeams.

Flexoelectric effect on the electroelastic responses of bending 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.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2012.0214

Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

In this paper, surface effects on the elastic behavior of static bending nanowires (NWs) are studied by using a comprehensive Timoshenko beam model. For NWs with different boundary conditions, explicit solutions are derived to study the combined effects of residual surface stress, surface elasticity and shear deformation on the effective stiffness and Young's modulus of the NWs. The stiffness is found to be size-dependent and this dependence is more significant for slender NWs. Residual surface stress tends to increase or decrease the stiffness of NWs depending on their boundary conditions, and the shear deformation always makes the NWs softer compared with the results of the Euler–Bernoulli beam model. The solutions agree well with experimental measurement in predicting the Young's modulus, especially for NWs with small length-to-thickness ratio. This work might be helpful for characterizing the mechanical properties of NWs and the design of nanobeam-based devices.

Zhi Yan

Papers

The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects

Surface effects on the electromechanical coupling and bending behaviours of piezoelectric nanowires

Flexoelectric effect on the electroelastic responses of bending piezoelectric nanobeams

Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

Timoshenko beam model for static bending of nanowires with surface effects