Transforming discrete movements of a sonar array into smooth vibration of a plate: Constant force input versus constant displacement input

Abstract

Numerical modeling of systems is an efficient way to explore new ideas, but an understanding of modeling assumptions as they relate to the actual physics of the system is critical. As a graduate student, I inherited a potentially revolutionary project involving sonar arrays. The idea was that grating lobes in the sound radiation from arrays could be eliminated by placing a plate between the array and the water. Grating lobes result from unintended, aliased superposition of traveling waves when discrete transducers attempt to create a single traveling wave in the array’s plane. The model initially assumed the transducers provided a constant displacement input to the plate’s vibration and the plate, thus, transformed the discrete traveling wave into a smooth continuous wave, resulting in elimination of grating lobes. The problem was that the plate’s impedance was higher than the transducers’ impedance and, thus, a constant force input was a better approximation to use in the model. When accurate assumptions were used, the grating lobes returned. A new idea was conceived to make something useful out of the original idea, though it required yet undeveloped materials. Although unexpected and disappointing at the time, “negative discoveries” can sometimes lead to positive ones.