Cheng Lei, Grosh Karl
Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48105-2125, USA.
J Acoust Soc Am. 2008 Jun;123(6):4152-64. doi: 10.1121/1.2908301.
Exact and approximate formulas for calculating the sensitivity and bandwidth of an electroacoustic transducer with an enclosed or trapped fluid volume are developed. The transducer is composed of a fluid-filled rectangular duct with a tapered-width plate on one wall emulating the biological basilar membrane in the cochlea. A three-dimensional coupled fluid-structure model is developed to calculate the transducer sensitivity by using a boundary integral method. The model is used as the basis of an optimization methodology seeking to enhance the transducer performance. Simplified formulas are derived from the model to estimate the transducer sensitivity and the fundamental resonant frequency with good accuracy and much less computational cost. By using the simplified formulas, one can easily design the geometry of the transducer to achieve the optimal performance. As an example design, the transducer achieves a sensitivity of around -200 dB (1 VmuPa) at 10 kHz frequency range with piezoelectric sensing. In analogy to the cochlea, a tapered-width plate design is considered and shown to have a more uniform frequency response than a similar plate with no taper.
推导了用于计算具有封闭或受限流体体积的电声换能器灵敏度和带宽的精确公式和近似公式。该换能器由一个充满流体的矩形管道组成，管道的一侧壁上有一个宽度逐渐变窄的板，模拟耳蜗中的生物基底膜。通过使用边界积分法，建立了一个三维流体-结构耦合模型来计算换能器的灵敏度。该模型用作寻求提高换能器性能的优化方法的基础。从该模型中导出了简化公式，以高精度且计算成本低得多的方式估计换能器的灵敏度和基频共振频率。通过使用这些简化公式，可以轻松设计换能器的几何形状以实现最佳性能。作为一个示例设计，该换能器在10 kHz频率范围内采用压电传感时实现了约-200 dB（1 V/μPa）的灵敏度。类似于耳蜗，考虑了一种宽度逐渐变窄的板设计，结果表明它比没有锥度的类似板具有更均匀的频率响应。
