Thermo-electro-mechanical Properties Of Piezoelectric Nanoplates With Flexoelectricity

Piezoelectric materials are widely used in sensors,actuators and other electronic components due to their inherent electro-mechanical coupling effect.With the development of micro and nano technology and the trend of structural miniaturization of intelligent devices,piezoelectric nano-materials,as the best material choice for micro and nano scale sensors,actuators,energy harvester and other electronic devices,have been the research focus and frontier.At micro and nano scale,a new electro-mechanical coupling effect,flexoelectric effect,has received much attention in recent years.Flexoelectric effect refers to the polarization caused by the strain gradient(or non-uniform strain),which is widely present in solid dielectrics(including piezoelectric materials),liquid crystals,and biomaterials.Flexoelectric effect has a significant size-dependent effect,which increases as the size of the structure decreases,so it will definitely affect the multi-field coupling characteristics and mechanical properties of the nano-scale piezoelectric materials and structures.Considering the flexoelectric effect and temperature effect,the thermo-electro-mechanical coupling characteristics and the static and dynamic mechanical behaviors of piezoelectric nano-plates are studied.Firstly,based on the flexoelectric theory and the Kirchhoff plate hypothesis,we derive the differential governing equation of piezoelectric nano-plates with thermo-electro-mechanical couplings.Then,we study the influence of the nonlinear terms in the governing equation,and finally use the Ritz method to obtain the transverse displacement and resonant frequency of the thin plates.In addition,the static and dynamic mechanical behaviors of functionally graded materials piezoelectric nano-plates considering the flexoelectric effect and temperature effect are studied.The effects of gradient index,temperature,flexoelectric coefficient and structural geometry on the bending and vibration behavior of functionally graded thin plates are discussed.In order to establish a more accurate mechanical model of thin plates consideringtemperature effect,this paper considers three models of material parameters,i.e,material parameters do not change with temperature,linearly change with temperature and nonlinearly change with temperature based on experimental data.The mechanical model and numerical simulation results established in this study will be helpful to further understand the multi-field coupling characteristics of micro and nano scale piezoelectric materials caused by flexoelectric effect,and will play a guiding role in the structural design and optimization of micro and nano electronic devices based on piezoelectric nano-plates.