音源面音圧のランダム分布が非線形場の形成に与える影響

摘要

The aim of the present report is to clarify the formation and behavior of sound pressure field from a statistical point of view when individual transducers in an array source have their performances or conversion efficiencies in a random manner. Linear as well as nonlinear fields are considered herein. To this end, we assume that the amplitudes and phases of pressure signals emitted from the transducers are random variables to obey Gaussian distribution functions and they are statistically independent. We also assume that the phase changes are small enough to be neglected. As expected, variation in field pressure due to the random distribution of source pressure are active in the nearfield. However, in the farfield, the theory proposed shows that the mean pressure amplitude of the fundamental component and its beam pattern are almost the same as the case where the pressure is distributed uniformly over the array aperture. On the other hand, the standard deviation around the mean is independent of the beam pattern and is inversely proportional to the square root of the number of transducers. For the second harmonics, both the average and variance of the pressure are dependent on the beam patterns. The validity of these theoretical findings is verified by computer simulation.%一般に，超音波トランスデューサの電気音響変換特性は個々に異なり，ばらつきが存在する。したがって，トランスデューサに同じ電圧を加えても，個々に発生する音圧の振幅および位相特性に相違が現れる。よって，このようなトランスデューサを多く配列してアレイ音源を構成した場合，そのトランスデューサに同一の電気信号を印加したときに形成される音場は，音源面音圧が一様として仮定した音場と異なることが予想される。本報告は，個々のトランスデューサの電気音響変換特性のばらつきが音場形成に果たしてどのような影響を与えるかを，線形場に限らず非線形高調波まで拡張して議論する。