A 3D meshless electromechanical model incorporating electrode inertia for accurate prediction of resonance characteristics in disk-type MEMS resonators

In this study, wave propagation in disk-type piezoelectric resonators is investigated by extending the polynomial modeling approach to incorporate electrode inertia. For sufficiently thin metallic electrodes, their elastic stiffness is neglected and only their mass contribution is retained. At both the top and bottom electrodes, the traction is assumed to balance the inertia of the respective electrode layers. This formulation modifies the axial boundary conditions, enabling accurate evaluation of the resonance and antiresonance frequencies (RFs and AFs). The results are compared with those obtained under the conventional stress-free assumption, demonstrating the significant influence of electrode inertia on the dynamic response. The effect of the thickness ratio, defined as the ratio of the driving electrode thickness to the piezoelectric film thickness, is further examined on longitudinal vibration frequencies and associated dispersion curves. It is shown that increasing the thickness ratio reduces both resonant and antiresonant frequencies. In addition, the presence of finite electrode thickness lowers the dispersion frequencies at a fixed mass ratio. These findings highlight the necessity of incorporating electrode inertia in the accurate modeling of MEMS disk resonators and provide reliable guidance for the design of devices requiring precisely controlled resonance characteristics.