CMUT modeling—extension to soft boundaries and thick plates
Bibliographic record
Abstract
Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo><</mml:mo> </mml:mrow> </mml:math> 0.5%), pull-in voltage (error <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo><</mml:mo> </mml:mrow> </mml:math> 2.3%), and resonance frequency (error <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo><</mml:mo> </mml:mrow> </mml:math> 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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".