Lobkis Oleg I, Chimenti D E
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, Illinois 61801, USA.
J Acoust Soc Am. 2003 Dec;114(6 Pt 1):3155-66. doi: 10.1121/1.1616927.
A plane-wave decomposition of collimated beams and electromechanical reciprocity relations are used to demonstrate fundamental differences and unusual similarities about transducer fields and transducer voltages at ultrasonic frequencies under various conditions. It is shown that the voltage induced by a transmitting acoustic piston transducer (constant particle velocity over the transducer surface) radiating into an ideal fluid medium on a second identical piston transducer, operating as a receiver, is nearly identical to the voltage observed when the two transducers have instead a Gaussian radial surface velocity distribution. The strong similarity in induced voltage begins when the two devices are separated by only several acoustic wavelengths, still well within the nearfield of both transducers, and the similarity increases with separation. Cases of transducer velocity distributions different from piston, such as Lorentzian or triangular, yield results nearly identical to the piston case. Transducers of differing size are also treated. It is further shown that an "equivalent transducer" can be derived for any combination of radiators, whose field is identical to the voltage measured using the pair. Moreover, with this concept the calculation of voltage in two-probe experiments is as simple as well-known approximations to the Rayleigh integral for a single transducer. These results have substantial consequences for calculations, either analytical or numerical, that predict the voltage measured in two-transducer experiments.
利用准直光束的平面波分解和机电互易关系，来展示在各种条件下超声频率下换能器场和换能器电压的基本差异和异常相似性。结果表明，发射声活塞换能器（换能器表面粒子速度恒定）向理想流体介质中辐射时，在作为接收器的第二个相同活塞换能器上感应出的电压，与两个换能器具有高斯径向表面速度分布时观测到的电压几乎相同。当两个器件仅相隔几个声波波长时，感应电压的强烈相似性就开始了，此时仍处于两个换能器的近场内，并且这种相似性随着间距的增加而增大。换能器速度分布不同于活塞的情况，如洛伦兹分布或三角形分布，产生的结果与活塞情况几乎相同。不同尺寸的换能器也在研究范围内。进一步表明，对于任何辐射器组合都可以导出一个“等效换能器”，其场与使用该对换能器测量的电压相同。此外，利用这一概念，双探头实验中电压的计算与单个换能器的瑞利积分的著名近似一样简单。这些结果对于预测双换能器实验中测量电压所进行的解析或数值计算具有重大影响。
