Modeling Electrode Thickness Effect in Piezoelectric Disc-Type Resonator: An Extended Polynomial Approach

A semi-analytical method is developed to study the free vibration of a cylindrical Micro-Electro-Mechanical Systems (MEMS) resonator, integrating Electrode Thickness (ET), by considering Electrode Inertia (EI), in the Polynomial Approach (PA). This analysis highlights the impact of Thickness Ratio (TR) on the characteristics of longitudinal waves in the Cylindrical Resonator (CR) that display radial modes, using the proposed Boundary Conditions (BC). Results show that the introduction of a non-zero ET shifts the normalized resonant and antiresonant frequencies, as noticeable in the Electro-Mechanical Coupling Coefficient (EMCC) and Dispersion Curves (DCs) compared to those of a previous study. Furthermore, illustrative examples show that the calculated normalized resonant and antiresonant cut-off frequencies exhibit a gradually growing reduction with increased TR and/or electrode density, resulting in decreased EMCC values. These comprehensive findings underscore the necessity of considering the TR influence for accurate analysis of CRs.