Modeling of high contrast partially electroded resonators by means of a polynomial approach

This work presents the modeling of high contrast partially electroded resonators by means of a polynomial approach. This method allows easily solving the equations that govern the structure. The boundary, symmetry, and continuity conditions are automatically incorporated into the equations of motion by the use of delta functions for the variables stress (T) and electric displacement (D) and appropriate analytical expression forms for the independent variables, mechanical displacements (u), and electric potential (ϕ). Structure symmetry was used to reduce the number of unknowns. For the zinc oxide (ZnO) resonator in extreme geometrical cases (thin plate and bar cases), a good agreement was obtained between the results of the proposed polynomial approach and those of an analytical approach for both the modal and harmonic analyses. The proposed polynomial approach was used to calculate the 2D resonator electrical admittance (full and partial metallization) near the 1D thickness fundamental mode, and the results highlight the presence of spurious modes. Influence of the metallization rate on the number of spurious modes in the bandwidth is studied. This model can also easily calculate the electromechanical coupling coefficient and the field profiles. Illustrations for both electromechanical coupling coefficient and particle displacement profiles are given for aluminium nitride (AlN), lead zirconate titanate, and ZnO resonators.