Modal and harmonic analyses of a MEMS piezoelectric resonator disc with a complete metallization

Orthogonal polynomial approach method has been extended in this paper to the modeling of a piezoelectric disc resonator in case of complete metallization with an excitation electrical source. This method makes use of Legendre polynomials series to express the mechanical displacement components and the electric potential which are introduced into the equations of motion of the piezoelectric structure. The formulation is founded on solving the Maxwell equations and three dimensional equations of linear elasticity coupled to the equation of motion. The principal advantage of this method consist of introducing, directly, the electrical source, the boundary and continuity conditions into the governing equations by the use of position-dependent physical constants and by a wise choice of the polynomial expansions for the independent variables, mechanical displacement components and electric potential. Both harmonic and modal analyses were studied, will have to define the resonance and anti-resonance frequencies, the input normalized electric admittance of the resonator disc, it is easy to implement for numerical calculation. A comparison of obtained results with analytical ones was provided.