Zhang Wen, Zhang Hui, Jin Shijiu, Zeng Zhoumo
State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China.
Micromachines (Basel). 2016 Mar 29;7(4):55. doi: 10.3390/mi7040055.
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.
电容式微机械超声换能器（CMUT）多层膜在包括发射效率和接收灵敏度在内的性能指标中起着重要作用。然而，对多层膜的研究很少。一些分析模型将多层膜简化为单层膜，这会导致不准确的结果。本文提出了一种用于具有多层膜的CMUT的新分析模型，该模型可以快速准确地预测多层膜在外部压力下的静态挠度和响应频率。推导基于里兹法和哈密顿原理。得到了外部压力、静态挠度和响应频率之间的数学关系。推导了相关的残余应力补偿方法。通过将其结果与有限元方法（FEM）模拟、实验数据以及将CMUT视为单层板/膜的其他单层模型进行比较，对三层和双层CMUT膜的模型进行了验证。对于三层CMUT膜，静态挠度曲线的相对误差范围为0.71%至3.51%，响应频率的相对误差范围为0.35%至4.96%。对于双层CMUT膜，采用残余应力补偿时，中心挠度的相对误差为4.14%，响应频率的相对误差为-1.17%。所提出的分析模型可为CMUT的设计和优化提供可靠的参考和准确的工具。
