中文摘要：

纳米科技的快速发展使压电纳米结构在纳米机电系统中得到广泛应用，形成了诸如纳米压电电子学等新的研究方向.与传统的宏观压电材料相比，在纳米尺度下压电材料往往呈现出不同的力学特性，而造成这种差异的原因之一便是表面效应.本文基于Stroh公式、Barnett-Lothe积分矩阵及表面阻抗矩阵，研究计入表面效应的任意各向异性压电半空间中的表面波传播问题，导出了频散方程.针对横观各向同性压电材料，假设矢状平面平行于材料各向同性面，发现Rayleigh表面波和B-G波解耦，并得到各自的显式频散方程.结果表明，Rayleigh表面波的波速小于偏振方向垂直于表面的体波，而B-G波的波速小于偏振方向垂直于矢状平面的体波.以PZT-5H材料为例，用数值方法考察表面残余应力和电学边界条件对表面波频散特性的影响发现：表面残余应力只对第一阶Rayleigh波有明显的影响；电学开路情形的B-G波比电学闭路情形的B-G波传播快.本文工作可为纳米表面声波器件的设计或压电纳米结构的无损检测提供理论依据.

英文摘要：

The fast developments in nanotechnology enable the wide applications of piezoelectric nano-structures in nano-electromechanical systems,forming new research directions such as nanopiezotronics.Compared with the traditional macroscopic piezoelectric materials,nano-scaled piezoelectric materials present di_erent mechanical properties,possibly due to the existence of surface e_ect,one of the main reasons for explaining the di_erence.This paper concerns the propagation of surface waves in a generally anisotropic piezoelectric half-space with surface e_ect.Stroh formalism,Barnett-Lothe integral matrices,and surface impedance matrices are adopted to theoretically derive the dispersion equations of surface waves.For transversely isotropic piezoelectric materials with the isotropic basal plane parallel with the sagittal plane,Rayleigh waves and B-G waves are found to be decoupled from each other,and their dispersion equations are derived in an explicit and compact form.It is rigorously shown that the velocity of Rayleigh waves should be smaller than that of the bulk waves polarized in the depth direction,whilst the velocity of B-G waves should be smaller than that of the bulk waves polarized in the direction perpendicular to the sagittal plane.In the numerical simulations,PZT-5H is taken as an example to numerically illustrate the influences of surface residual stress and electrical boundary conditions on the dispersion properties of surface waves.It is found that surface residual stress has a significant e_ect only on the first-order Rayleigh wave,and the B-G wave under the electric open-circuit condition propagates faster than under the electric closed-circuit condition.The theoretical predictions and numerical results presented in the paper should be helpful in understanding size-dependent dynamic behaviors of piezoelectric structures with surface e_ect and may provide a solid basis for the design of nano-sized surface acoustic wave devices as well as for the nondestructive testing of nano-sized piezoelectric structur