Vibration of annular plate concentrators with conical cross-section

In this paper, the torsional vibration and radial vibration of isotropic metal thin annular plates with conical cross-section are deduced by using Bessel functions; and according to electro-mechanical analogy, the electro-mechanical equivalent circuits are obtained. Based on the electro-mechanical equivalent circuits, the resonance frequency equations and the expressions of angular and radial displacement amplitude magnifications are derived, and the resonance frequencies and magnifications are solved by analytical method. The relationships between torsional and radial resonance frequencies and geometrical dimensions are discussed; and the relationships between angular and radial displacement amplitude magnifications and the ratio of outer radius over inner radius are analyzed. Modal shapes are analyzed by finite element method (ANSYS). It is shown that the values calculated by using the theory of this paper are in good agreement with the results simulated by ANSYS. The method can serve as benchmark values for researchers to validate other variable thickness thin annular plates.