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A double Legendre polynomial quadrature-free method was presented to analyze axisymmetric free vibration problem for axially polarized Functionally Graded Piezoelectric circular plates. The present analytical method directly incorporated the boundary conditions into the vibration control equation. At the same time, the mechanical displacements and the electrical potential were defined as the form of double Legendre polynomials series. Then, the solution of eigenvalue was used to obtain the resonant/anti-resonant frequencies. In view of including lots of time-consuming integration calculations, the quadrature-free process was deduced to improve the computational efficiency. The valid of the presented method was verified by the comparison with the existing literature and the commercial software COMSOL. Furthermore, the effects of the material gradient index, radius-thickness ratio on the frequencies, and electro-mechanical coupling efficient were studied. The results showed that the frequency-radius product tends to be stable with the increase of the radius-thickness ratio, and the increase of gradient index led to the increase of the frequency-radius product. [ABSTRACT FROM AUTHOR]

For the purpose of design and optimization for piezoelectric quasi-crystal transducers, guided waves in a functionally graded 1-D hexagonal piezoelectric quasi-crystal plate are investigated. In this paper, a model combined with the Bak's and elastohydrodynamic models is utilized to derive governing equations of wave motion, and real, pure imaginary, and complex roots of governing equations are calculated by using the modified Legendre polynomial method. Subsequently, dispersion curves and displacements of phonon and phason modes are illustrated. Then, guided waves in functionally graded 1-D hexagonal piezoelectric quasi-crystal plates with different quasi-periodic directions are studied. And the phonon-phason coupling effect on Lamb and SH waves are analyzed. Accordingly, some interesting results are obtained: The phonon-phason coupling just affects Lamb waves in the x - and z -direction quasi-crystal plates, and SH waves in the y -direction quasi-crystal plate. Besides, frequencies of propagative phason modes decrease as phonon-phason coupling coefficients Ri increase. Furthermore, a variation in the polarization has a more significant influence on phonon modes, and a variation in the quasi-periodic direction has a more significant influence on phason modes. [ABSTRACT FROM AUTHOR]