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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]

This article presents an extension of the double Legendre polynomial method to model and evaluate the axisymmetric free vibration problem for the axially polarized piezoelectric resonator. The aim is to show the benefit of the employed method. The polynomial series was used to define the mechanical displacements and electrical potential at the same time. The proposed approach considerably improves computing efficiency by avoiding much of the numerical integration calculations. As a result, the electromechanical coupling coefficient shows that the fundamental mode is the most piezoactive mode in the structure. Furthermore, the electrical input impedance and field profiles are easily presented. [ABSTRACT FROM AUTHOR]

The Legendre polynomial approach has been proposed to solve wave propagation in multilayered flat plates and functionally graded structures for more than ten years, but it can deal with a multilayered plate only when the material properties of two adjacent layers do not change significantly. In this paper, an improvement of the Legendre polynomial approach is proposed to solve wave propagation in what, from now on, we will call general multilayered piezoelectric cylindrical plates, to mean indifferently with or without very dissimilar materials. Detailed formulations are given to highlight the differences from the conventional Legendre polynomial approach. Through numerical comparisons among the exact solution (from the reverberation-ray matrix), the conventional polynomial approach, and the improved polynomial approach, the validity of the proposed approach is illustrated. Then, the influences of the radius-to-thickness ratio on the dispersion curves, the stress, and electric displacement distributions are discussed. It is shown that the conventional orthogonal polynomial approach cannot obtain correct continuous normal stress and normal electric displacement shapes, unlike the improved orthogonal polynomial approach, which overcomes these drawbacks. It is also found that three factors determine the distribution of mechanical energy and electric energy at higher frequencies: the radius-to-thickness ratio, the wave speed of component material, and the position of the component material. [ABSTRACT FROM PUBLISHER]