Modeling of a Circular Ring MEMS Resonator with Voltage Excitation by Means of an Orthogonal Polynomial Method

The three-dimensional vibrational behavior of a piezoelectric circular ring made of a 6 mm hexagonal material is studied using Legendre polynomial method. The method is simple to implement and based on expanding the electrical potential and the mechanical displacement components in a double series of an orthonormal basis made up of Legendre polynomials. In addition to Maxwell equations, three governing equations of motion are written and then converted into a matrix eigenvalue problem taking into account the presence of an electrical source. Numerical calculations are carried out in order to highlight the capabilities of the method in both free and forced vibration analysis. With a single calculation, the method restitutes all the resonance and anti-resonance frequencies whatever their order, the normalized electric admittance and the mechanical field profiles. The developed model is validated via a comparison of our results with their counterparts reported in the literature, a high accuracy is obtained.