A fast computational method for modeling and simulation of large projector arrays is presented. The method is based on the array equations that account for the acoustic interaction among the projector elements as well as the individual characteristics of each projector. Unlike the existing solution method in which the acoustic interaction must be known a priori in the form of interaction impedance matrix Z, the present method seeks the solution of modified array equations through iterations without explicitly evaluating the Z matrix. This significantly speeds up the analysis of complex arrays with surrounding structures, where the evaluation of the Z matrix may require a large number of time-consuming finite element computations. The method is compared with the traditional Z-matrix method for the case of a cylindrical array of 72 × 8 Tonpilz transducers. For the same level of accuracy, the iterative method is shown to be up to 2 orders-of-magnitude faster than the Z-matrix method. The method can be used for rapid design and analysis of active sonar arrays and medical ultrasonic transducers, often made of hundreds and even thousands of elements.

The array equations are commonly used for analysis and conceptual design of active sonar projector arrays. Calculation of the radiation impedance matrix poses a major computational bottleneck for the solution of the array equations, which leads to a dramatic increase in computational load as the number of constituent transducers increases. Here, we propose an iteration-based solution method that does not require the calculation of the radiation impedance matrix, as a computationally efficient alternative to the status quo. The validity of the iteration-based analysis is judged against the full finite-element analysis that includes the entire array as well as the medium. The array equations for the 1/3-sector of a cylindrical array comprised of 48 Tonpilz transducers are augmented by the lumped element models, and are solved iteratively for the acoustic and electro-mechanical characteristics. The iteration-based analysis exhibits rapid convergence and accuracy comparable with the FE analysis. Simulations also reveal that the acoustic coupling between transducers has more pronounced effects on the electro-mechanical characteristics of individual transducers than the acoustic performance of the array.

With the introduction of low-frequency active sonar in anti-submarine warfare, there is a growing need for a novel underwater invisibility device that could replace the existing passive anechoic tiles. In this talk, we describe an experiment on active reduction of underwater echoes at low frequencies using an array of tile-shaped projectors. Each tile projector was designed with the aid of finite-element computations and tested in an acoustic tank for transmit voltage sensitivity and directivity. An array of tile projectors, covering a scale model submarine in a large acoustic tank, were driven by control signals that were intended to produce the impedance match between water and the object. Depending on the frequency of the incident wave, echo reduction as large as 6 dB was achieved. [This work has been supported by the Low Observable Technology Research Center program of Defense Acquisition Program Administration and Agency for Defense Development.]

Uniformity in transducer performance is a must-have to ensure the reliable acoustic performance of a tile projector, used for active echo reduction. However, practical limitations imposed by variations in material properties and fabrication errors lead to performance variations among unit transducers, which could degrade the radiation characteristics (transmitting voltage response and directivity) of the tile projector and ultimately the echo reduction performance. In this paper we present a method to minimize these adverse effects via an appropriate placement of unit transducers within the tile projector. To this end, we perform a series of coupled acoustic-piezoelectric simulations, assuming a group of 36 unit transducers having 6 dB variations in transmitting voltage response, to analyze and compare the radiation characteristics of tile projectors under different transducer placement schemes.

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