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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 ([lowercase_phi_synonym]). 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. [ABSTRACT FROM AUTHOR]

A bidimensional analysis of 6 mm hexagonal resonators is described using a double orthonormal basis set for the expansion of field quantities. The analysis takes into account the electrical voltage source and by means of a unique formalism along with a single calculation restitutes all the types of resonance whatever the thickness to width ratio value through either modal solutions or electrical impedance. An illustrative example gives the capabilities of the method to investigate spurious modes in laterally bounded resonators. [ABSTRACT FROM AUTHOR]

The Legendre polynomial method has been extended to the modeling of bulk acoustic wave (BAW) resonators. Modifications have been made to the formulation in order to account for large differences in the physical properties of adjoining layers and to take into account the electric source. A unique formalism has been obtained which allows for both harmonic and modal analyses. Resonance and antiresonance frequencies, electric input impedance, electromechanical coupling coefficients, and quality factors have been obtained for an aluminum/zinc oxide/aluminum (Al/ZnO/Al) BAW resonator. The results are in excellent agreement with analytical results. [ABSTRACT FROM AUTHOR]