With the purpose of integrating new functionalities in micro electro mechanical resonators, frequency response of such resonators has been gained more importance since long time ago. Previous studies have only concentrated on geometries with full metallization and centralized partial metallization. This paper proposes a study of wave propagation, in case of a homogeneous circular disk excited by an AC electrical source with partial annular metallization using Legendre polynomial approach. Our study consists of solving equation of motion and characteristic equations of piezoelectricity with appropriate boundary and continuity conditions. Numerical calculation provides both modal and harmonic analysis, whatever the mode order. In addition to dispersion curves, mechanical and electrical dispersion profiles were presented in a 3D configuration. The impact of varying metallization rates on resonance frequencies is highlighted. The validity of Legendre polynomial method is confirmed through a comparison between polynomial and analytical results provided in the literature.