SURFACE WAVES IN A PIEZOELECTRIC HALF-SPACE WITH SURFACE EFFECT

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 different mechanical properties, possibly due to the existence of surface effect, one of the main reasons for explaining the difference. This paper concerns the propagation of surface waves in a generally anisotropic piezoelectric half-space with surface effect. 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 effect 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 effect 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 structures.