考虑挠曲电效应的压电纳米薄板力-电-热耦合特性研究

摘要：挠曲电效应是由应变梯度引起的，与尺度相关的力电耦合效应。基于Kirchhoff板假设和挠曲电理论，本文推导了温度和电压作用下的压电薄板力-电-热耦合微分控制方程，定量分析了微分控制方程中非线性项的影响，并针对四周固支压电薄板采用Ritz法求解，数值计算了压电薄板的弯曲和振动行为。在研究温度和挠曲电效应对薄板耦合特性和力学行为的影响时，本文分别考虑了材料系数不随温度变化和随温度线性变化两种情况。以PZT-5H为例，我们讨论了挠曲电和温度对压电薄板的横向位移和固有频率的影响。研究结果表明挠曲电效应对压电纳米薄板的力学行为影响很大，且具有明显的尺寸效应。此外，薄板对温度变化非常敏感。因此，可通过挠曲电效应和温度来调控压电纳米薄板的多场耦合特性和力学行为，进而优化基于压电薄板的NEMS/MEMS中传感器、作动器等电子器件的性能。

Thermo-electro-mechanical properties of piezoelectric nanoplates with flexoelectricity

Abstract：Flexoelectric effect, which is induced by inhomogeneous strain (or strain gradient), is a size-dependent electromechanical coupling effect. Based on the Kirchhoff plate hypothesis and the theory of flexoelectricity, the differential governing equations of the piezoelectric thin plates under temperature and voltage are derived. The influence of nonlinear terms in governing equations is quantitatively analyzed. For clamped piezoelectric nanoplates, the governing equations are solved by adopting Ritz’s method, and the bending and vibration behaviors of the piezoelectric nanoplates are numerically investigated. To study the influence of temperature and flexoelectricity on the coupling characteristics and mechanical behavior of thin nanoplates, we consider the material coefficients of the piezoelectric nanoplates being independent on temperature and linearly dependent on temperature, respectively. For case studies, we choose PZT-5H as the structural material and investigate the influence of flexoelectricity and temperature on the transverse displacement and resonant frequency of the nanoplates. Results show that flexoelectric effect has a significant influence on the mechanical behavior of piezoelectric nanoplates and is size-dependent. In addition, the thin nanoplate is sensitive to the temperature change. Therefore, we can utilize flexoelectricity and temperature to tune the multi-field coupling characteristics and mechanical behavior of piezoelectric nanoplates , in this way，the performance of piezoelectric nanoplate based electronic devices such as sensors and actuators in NEMS/MEMS could be optimized.