A finite element approach to modelling fractal ultrasonic transducers
A finite element approach to modelling fractal ultrasonic transducers
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DOI：
10.1093/imamat/hxv012
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发表时间：
2015-12
影响因子：
1.2
通讯作者：
E. A. Algehyne;A. Mulholland
中科院分区：
文献类型：
--
作者：
E. A. Algehyne;A. Mulholland
压电超声换能器通常采用复合材料结构以提高其发射和接收灵敏度。复合材料的几何形状是规则的，具有一个主要的长度尺度，并且由于这些是谐振装置，这决定了装置的中心工作频率。为了构造宽带装置，因此利用跨越一定范围的长度尺度的谐振器似乎是自然的。在这篇文章中，我们推导出一个数学模型来预测分形超声换能器的动态;在这种情况下的分形Sierpinski垫片。包含在该结构中的电场和机械场的表达式用有限元基础来表示。然后分析超声波在该换能器中的传播，并用于导出作为驱动频率的函数的无量纲电阻抗和发射和接收灵敏度的表达式。将这些关键性能指标与等效标准（欧几里德）设计进行比较，显示了这些分形设计的一些优点。
Piezoelectric ultrasonic transducers usually employ composite structures to improve their transmission and reception sensitivities. The geometry of the composite is regular with one dominant length scale and, since these are resonant devices, this dictates the central operating frequency of the device. In order to construct a wide bandwith device it would seem natural therefore to utilize resonators that span a range of length scales. In this article we derive a mathematical model to predict the dynamics of a fractal ultrasound transducer; the fractal in this case being the Sierpinski gasket. Expressions for the electrical and mechanical fields that are contained within this structure are expressed in terms of a finite element basis. The propagation of an ultrasonic wave in this transducer is then analyzed and used to derive expressions for the non-dimensionalised electrical impedance and the transmission and reception sensitivities as a function of the driving frequency. Comparing these key performance measures to an equivalent standard (Euclidean) design shows some benefits of these fractal designs.