Full dispersion and characteristics of complex guided waves in functionally graded piezoelectric plates

Abstract

The improvement of the resolution and energy conversion efficiency of piezoelectric devices requires a thorough study of guided wave, especially the evanescent wave modes with high-phase speed and low attenuation. Due to the computation difficulties, investigations about the evanescent wave in piezoelectric structures are rather limited. In this article, an analytic method based on the orthogonal function technique is presented to investigate the complex dispersion relations and the evanescent guided wave in functionally graded piezoelectric plates, which can convert the complex partial differential equations with variable coefficients into an eigenvalue problem and obtain all solutions. Comparisons with other related studies are conducted to validate the correctness of the presented method. Three-dimensional full dispersion curves are plotted to gain a better insight into the nature of the evanescent waves. The influences of piezoelectricity and graded fields and electrical boundary conditions on evanescent waves are illustrated. The electromechanical coupling factors of the functionally graded piezoelectric material plates with different gradient fields are also investigated. Furthermore, the displacement amplitude and electric potential distributions are also discussed to illustrate the specificities of evanescent guided waves. The corresponding results presented in this work are promised to be used to improve the resolution of piezoelectric transducers.