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.

The research on the propagation of surface waves has received considerable attention in order to improve the efficiency and natural life of the surface acoustic wave devices, but the investigation on complex Rayleigh waves in functionally graded piezoelectric material (FGPM) is quite limited. In this paper, an improved Laguerre orthogonal function technique is presented to solve the problem of the complex Rayleigh waves in an FGPM half-space, which can obtain not only the solution of purely real values but also that of purely imaginary and complex values. The three-dimensional dispersion curves are generated in complex space to explore the influence of the gradient coefficients. The displacement amplitude distributions are plotted to investigate the conversion process from complex wave mode to propagating wave mode. Finally, the curves of phase velocity to the ratio of wave loss decrements are illustrated, which offers extra convenience for finding the high phase velocity points where the complex wave loss is near zero.

Functionally graded piezoelectric–piezomagnetic (FGPP) material simultaneously consists of piezomagnetic and piezoelectric phases, which are able to convert energy among mechanical, electric, and magnetic fields. The magneto-electric effect on waves in FGPP fan-shaped cylindrical structures is studied by exploiting the double Legendre orthogonal polynomial method. By means of the Heaviside function, the initial conditions are brought into wave motion equations. Dispersion properties, electric and magnetic potential, and the Poynting vector are calculated. Subsequently, the effect of the graded variation and geometric size on wave characteristics is analyzed. The FGPP fan-shaped cylindrical structures are of complex geometrical shape and material inhomogeneity, so their influences on the magneto-electric effect are the focus of discussion. Results reveal that the cut-off frequencies have a negative relationship with the cross-section area of the structure. The magneto-electric effect could be adjusted via altering the geometric size of the cross-section. These results can be utilized to design and optimize piezoelectric–piezomagnetic fan-shaped transducers.