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Micromachines 2016, 7(4), 55; doi:10.3390/mi7040055

An Analytical Model for CMUTs with Square Multilayer Membranes Using the Ritz Method

State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China
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Academic Editors: Marc Desmulliez and Joost Lötters
Received: 22 December 2015 / Revised: 21 March 2016 / Accepted: 22 March 2016 / Published: 29 March 2016
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Abstract

Capacitive micromachined ultrasonic transducer (CMUT) multilayer membrane plays an important role in the performance metrics including the transmitting efficiency and the receiving sensitivity. However, there are few studies of the multilayer membranes. Some analytical models simplify the multilayer membrane as monolayer, which results in inaccuracies. This paper presents a new analytical model for CMUTs with multilayer membranes, which can rapidly and accurately predict static deflection and response frequency of the multilayer membrane under external pressures. The derivation is based on the Ritz method and Hamilton’s principle. The mathematical relationships between the external pressure, static deflection, and response frequency are obtained. Relevant residual stress compensation method is derived. The model has been verified for three-layer and double-layer CMUT membranes by comparing its results with finite element method (FEM) simulations, experimental data, and other monolayer models that treat CMUTs as monolayer plates/membranes. For three-layer CMUT membranes, the relative errors are ranging from 0.71%–3.51% for the static deflection profiles, and 0.35%–4.96% for the response frequencies, respectively. For the double-layer CMUT membrane, the relative error with residual stress compensation is 4.14% for the central deflection, and −1.17% for the response frequencies, respectively. This proposed analytical model can serve as a reliable reference and an accurate tool for CMUT design and optimization. View Full-Text
Keywords: capacitive micromachined ultrasonic transducer (CMUT); multilayer membrane; static deflection; frequency response; residual stress compensation capacitive micromachined ultrasonic transducer (CMUT); multilayer membrane; static deflection; frequency response; residual stress compensation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Zhang, W.; Zhang, H.; Jin, S.; Zeng, Z. An Analytical Model for CMUTs with Square Multilayer Membranes Using the Ritz Method. Micromachines 2016, 7, 55.

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