Static and Dynamic Analysis of a Piezoelectric Semiconductor Cantilever Under Consideration of Flexoelectricity and Strain Gradient Elasticity

In this work, the static and dynamic response of a piezoelectric semiconductor cantilever under the transverse end force with consideration of flexoelectricity and strain gradient elasticity is systematically investigated. The one-dimensional governing equations and the corresponding boundary conditions are derived based on Hamilton's principle. After that, combining with the linearized equations for the conservation of charge, the effects of characteristic length and flexoelectric coefficient on the working performance of a ZnO nanowire are demonstrated as a numerical case, including the static mechanical and electric fields, natural frequencies, and the frequency-response characteristics at resonances. The results indicate that the flexoelectric effect has a great influence on the electric properties of the nanowire, while the strain gradient effect directly contributes to its mechanical properties. To some extent, the increase in characteristic length is equivalent to the stiffness strengthening. The qualitative results and quantitative data are beneficial for revealing the underlying physical mechanism and provide guidance for the design of piezoelectric semiconductor devices.