Distribution of the Clamped Boundary and Its Impact on Resonator Performance

Capacitive resonator performance including sensitivity is determined by its capacitive change and resonant frequency shift in response to an external perturbation such as added mass. Conventional designs are inherently defined by fully clamped boundaries around the deflectable plate. However, recent advances suggest that bilateral and quadrilateral concentric boundary resonators can offer improved performance through enhanced deflection compared to conventional fully clamped resonators. This work analyses how the spatial distribution of clamped boundaries under identical total clamped angles affects key resonator metrics including sensitivity, which is manifested through change in capacitance and frequency shift in electrical characterization. Resonators with bilateral and quadrilateral clamped boundary configurations are the focus of this work to demonstrate the idea. In order to do this, resonators with total clamped angles of 120°, 180°, and 240° are fabricated and characterized using electrical impedance analysis, with results in agreement with the conducted finite element analysis. The quadrilateral configurations outperformed bilateral ones in both frequency shift and capacitance change, indicating that clamped boundary distribution serves as a critical design parameter. These findings offer new insight into structural optimization strategies for capacitive resonators beyond conventional clamping schemes.