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The paper presents a semi-analytical method, named the Double Legendre Polynomial Method (DLPM), which is extended for modeling the axisymmetric free vibration of a functionally graded piezoelectric (FGP) hollow cylinder resonator. The FGP resonator is composed of two-phase graded piezoelectric materials, Lead zirconate titanate (PZT4) and aluminum nitrid (AlN), on the top and bottom surfaces, respectively, where the material properties gradually change along the thickness direction. The integration of FGP materials with piezoelectric materials is an innovative aspect in material science, and this paper explores their dynamic behavior, providing insights into their mechanical and electrical properties and contributes to expand our understanding of the axisymmetric free vibration of FGP hollow cylinder resonators as a crucial factor for optimizing their performance across a wide range of applications, including sensors, actuators, energy harvesting, and structural health monitoring systems. The DLPM is applied to solve the wave governing differential equations of motion, offering a new tool for studying the dynamic behavior of FGP hollow cylinders under axisymmetric vibration. The study investigates the effects of the diameter-thickness ratio on the effective electromechanical coupling coefficient and the resonant and anti-resonant frequencies of the FGP hollow cylinder. The results show that as the diameter-thickness ratio increases, the frequency-diameter product appears to become more stable. This observation is a valuable insight for optimizing the design of these resonators. Furthermore, the study presents the electrical input admittance, the natural frequencies as well as the mechanical displacement and electric potential profiles of the resonator. All the provided results are based on the calculation of the resonant frequencies. The validity of the presented results was verified by the comparison with the existing ones reported in the literature. [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]