CMUT modeling - extension to soft boundaries and thick plates

The Classical Kirchhoff–Love plate theory is widely used to model capacitive micromachined ultrasonic transducer (CMUT) cells, assuming thin plates with negligible shear deformation and rigid boundaries. However, thicker polymer-based CMUTs operate beyond the limits of these assumptions, where the shear and boundary effects become significant. These factors alter the displacement profile, lowering the resonant frequency and the static pull-in voltage. Existing analytical models do not consider these effects alone or in combination. This study introduces the softly-clamped displacement equation, which accounts for both shear deformation and compliant boundary behavior using only two fitting constants for a single cell. The aspects investigated include the plate deflection, pull-in voltage, and electromechanical coupling coefficient. The model was validated against finite element model (FEM) simulations across various thickness-to-radius ratios, applied pressures, and voltages. The proposed reduced-order model was implemented in SPICE for both large- and small-signal operating regimes and showed excellent agreement with the FEM results: pull-in displacement (error < 0.5%), pull-in voltage (error < 2.3%), and resonance frequency (error < 4.2%). The softly-clamped model bridges a critical gap in CMUT modeling and offers a scalable framework for designing thick-plate, polymer-based transducers under realistic boundary conditions.