Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Mechanical and Materials Engineering


Dr. Liying Jiang


Piezoelectric beam- and plate-based nanostructures hold a promise for device applications in the nanoelectromechanical systems (NEMS) due to their superior mechanical and electromechanical coupling properties. “Small is different”, nanostructured piezoelectric materials exhibit size-dependent properties, which are different from their bulk counterparts. For predicting the unique physical and mechanical properties of these novel nanostructures, continuum mechanics modeling has been regarded as an efficient tool. However, the conventional continuum models fail to capture the size effects of nanostructures and thus are not directly applicable at the nanoscale. Therefore, it is necessary to develop modified continuum models for piezoelectric nanostructures by incorporating the size effects and investigate the size-dependent properties of piezoelectric nanostructures based on the developed models.

Nanoscale structures are characterized by a high surface to volume ratio. The atoms in the surface layers of a structure are exposed to a different environment compared to those in the bulk of the structure. Thus, surface has a considerable influence on the physical and mechanical behaviors of nanoscale structures and is believed to be responsible for their size-dependent properties. In addition, for nanostructured piezoelectric materials, the strain gradient induced flexoelectricity could be significant and contribute to their size-dependent properties. In this thesis, the influence of the surface effects and flexoelectric effect on the mechanical and electrical properties of piezoelectric nanostructures is investigated through modified continuum models. Firstly, based on a surface piezoelectricity model and the generalized Young-Laplace equations, modified continuum models with surface effects are developed to investigate the bending, vibration, buckling behaviors and electromechanical properties of piezoelectric nanobeams and nanoplates with different boundary conditions. Next, by accounting for the flexoelectric effect through the extended linear theory of piezoelectricity and conventional beam models, the static and dynamic responses of piezoelectric nanobeams are presented. It is demonstrated from this study that the size effects prominently influence the mechanical behaviors and the electroelastic responses of piezoelectric nanostructures.

This research carries out a theoretical methodology to predict the static bending, electroelastic field distribution, resonant frequencies of vibration and critical electric potential for the mechanical buckling of piezoelectric nanostructures with different structure geometries, loading conditions and boundary conditions, which is expected to provide a fundamental understanding on the electromechanical coupling behavior of piezoelectric structures at the nanoscale. It is helpful for understanding the size-dependent properties of nanostructured piezoelectric materials and performance improvement of the beam- and plate-based electronic devices in NEMS.