Electronic Thesis and Dissertation Repository


Master of Engineering Science


Mechanical and Materials Engineering


Liying Jiang


With the development of nanotechnology, piezoelectric nanostructures have attracted a surge of interests in research communities for the potential applications as transistors, sensors, actuators, resonators and energy harvesters in nanoelectromechanical systems (NEMS) due to their high electromechanical coupling and unique features at the nano-scale. Piezoelectric nanomaterials have been characterized to possess size-dependent electromechanical coupling properties from both experimental and theoretical perspectives. Therefore it is of great importance to investigate the physical mechanisms of these distinct nano-scale structure features in order to fulfill the design and application of those piezoelectricity-based nanodevices.

Due to large surface to volume ratio and manifest strain gradients typically present in nanostructures, surface effects and flexoelectricity are commonly believed to be responsible for the size-dependent electromechanical properties of piezoelectric nanomaterials. This thesis aims to develop modified continuum mechanics models with the consideration of the surface effects and the flexoelectricity to theoretically investigate such size effects. Based on the classical Kirchhoff plate model and the extended linear piezoelectricity theory, the influence of flexoelectricity on the static bending and the transverse vibration of a piezoelectric nanoplate (PNP) is firstly examined. Then the surface effects including the residual surface stress, the surface elasticity and the surface piezoelectricity are further incorporated to develop a more comprehensive modified Kirchhoff plate model in addition to the flexoelectricity. Variational principle is adopted to derive the governing equations and the corresponding boundary conditions for a clamped PNP.

Ritz approximate solutions for the static bending and the free vibration of the PNP indicate that the influence of the flexoelectricity and the surface effects is more prominent for thinner plates with smaller thickness. The simulation results also demonstrate that such size effects on the electromechanical coupling behaviors of the PNP are sensitive to the surface material properties, the applied electrical load and the plate dimensions. Moreover, it also suggests that the possible frequency tuning of PNP-based resonators through the applied electric voltage could be modified by either the flexoelectricity or the surface effects.

The current work is claimed to provide increased understanding on the fundamental physics of the size-dependent electromechanical coupling properties of piezoelectric nanostructures and thus benefit the design and applications of PNP-based nanodevices.