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In this paper, we report an extension of a polynomial and numerical vibrational characterization of an annular piezoelectric disc resonator partially covered with electrodes. The three governing partial differential equations of motion are solved to provide the frequency response of the piezoelectric disc using a polynomial approach. This method makes use of Legendre polynomials series to express the mechanical displacement components and the electrical potential which are introduced into the equations of motion of the piezoelectric structure. The principal advantage of this method consists of incorporating the electrical source, the boundary and continuity conditions directly 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, the mechanical displacement components and the electrical potential. Both harmonic and modal analyses were studied and are presented. Numerical calculations based on the foregoing method were performed to present resonance and anti-resonance frequencies, electromechanical coupling coefficient, field profiles and electrical input admittance for PIC151 and PZT5A disc resonators with various metallization rates. The high accuracy and reliability of our approach is confirmed via a comparison of our results with their counterparts reported in literature.