考虑表面效应的压电纳米结构的波动问题研究

The applications of micro/nano piezoelectric structure in modern micro /nanoelectromechanical system, including surface acoustic wave and bulk acoustic wave devices, is increasing more widely recently. However, when the structure size is reduced to nanometer scale, surface effect have a significant impact on the macroscopic mechanical performance (like wave properties) in the structure, the traditional continuum theory is no longer applicable. For micro/nano piezoelectric structure, combined with the classical continuum theory, this project establishes the surface electroelasticity theory, and extends this theory to the bulk wave field. Using the new non classical surface electroelasticity theory, the theoretical analysis on piezoelectric structure is developed. Utilizing the simplified theory, the state space method and the displacement potential function method, we will construct the formulations for wave propagating in piezoelectric structures. And the effect of mechanical, electrical field and the coupling effect, material inhomogeneous, and geometric parameters on piezoelectric structure is discussed. The effect of surface parameters (material parameters, thickness) on acoustic character (dispersion, group velocity, displacement distribution) is emphasized. Through this project, we will develop a series of exact solutions and analytical solutions of bulk wave, and present a benchmark for various approximate theories and numerical methods, and serve for the innovation of piezoelectric nanostructures and optimization design.

压电纳米结构在现代微/纳机电系统中的应用日益广泛，在声表面波、体波器件中也有大量应用。然而当结构尺寸减小到微纳米尺度时，表面效应对结构的宏观力学性能（如波动特性）有显著影响，传统的连续介质模型已不再适用。本项目针对微纳米压电结构，结合经典连续介质体系，建立考虑表面效应的表面电弹性理论，从而将非经典表面电弹性理论拓展到体波波动领域。利用全新的表面电弹性理论，对压电结构开展波动分析的理论研究：利用简化理论、状态空间法和势函数法等，构造考虑表面效应的压电结构波动分析列式；考虑力电场及耦合作用、材料非均匀、几何参数等的影响；重点分析表面参数（材料参数、厚度）对声场特性（弥散、群速度、位移分布等）的影响。通过本项目研究，拟发展出一系列关于体波波动问题的精确解、解析解，使之成为检验各种简化理论和数值方法的基准，并为压电纳米结构的创新构思以及优化设计服务。

现代微、纳机电系统应用日益广泛，而耦合了机械场和电场的压电纳米结构也格外受人瞩目。然而当结构尺寸减小到微纳米尺度时，表面效应对结构的宏观力学性能有显著影响，传统连续介质模型失效。本项目结合经典连续介质体系，建立考虑表面效应的表面电弹性理论，将非经典表面电弹性理论拓展到体波波动领域。利用建立的表面电弹性理论，对压电结构开展波动分析的理论研究：利用简化理论，构造考虑表面效应的压电结构波动分析列式；考虑力电场及耦合作用、几何参数等的影响；重点分析表面参数（如厚度）对声场特性（弥散、相速度等）的影响。通过本项目研究，发展出关于体波波动问题的精确解、解析解，使之成为检验各种简化理论和数值方法的基准，并为压电纳米结构的创新构思以及优化设计服务。