Relationship between geometric features and vibration characteristics in functionally graded piezoelectric annular plates: An extended double Legendre polynomial method

The utilization of flexural, longitudinal, and torsional modes in functionally graded piezoelectric (FGP) annular plates depends on their geometric features. The investigation of the relationship between geometric features and vibrational characteristics offers valuable insights for optimal design. In this paper, the double Legendre polynomial method (DLPM) is extended for the first time to study the three-dimensional (3D) flexural vibration of FGP annular plates from two-dimensional (2D) axisymmetric vibration based on 3D elasticity theory. The validity of the proposed method is verified by literature results and finite element method (FEM) results. The influence of the relationship between the radial wall thickness and the height on the flexural, longitudinal and torsional vibrations of FGP annular plates is systematically revealed. The results provide comprehensive guidance for the design and application of FGP annular plates in domains requiring high precision, high stability, and high sensitivity.