Iterative solutions of the array equations for rapid design and analysis of large projector arrays

Abstract

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.

Modeling and Design of a Rear-Mounted Underwater Projector Using Equivalent Circuits

“…The main difference between our EC analysis and FEA is that the 2-D axis-symmetric finite element model involved a coupled vibration of all components of our basic model ( Figure 2) due to the comparable dimensions in the axial and lateral directions. For thin head mass models that possibly apply a noticeable effect of flexural resonance mode near the fundamental mode, EC models with an additional resonance branch or FEA can be used for higher accuracy [5,6]. Despite the higher accuracy of the FEA compared to the EC model, the results obtained in this study imply that the EC model was advantageous over the FEA in terms of the speed and efficiency of the analysis.…”

“…The flexural resonance frequency highly depends on the head mass thickness, as shown in the approximated expression in Equation 3, where c h , t h , D h , and ν h denote the wave speed, thickness, diameter, and Poisson's ratio of the head mass, respectively [1]. The mode coupling with a flexural mode typically lowers the longitudinal resonance frequency (f 2 ) [5,6].…”

“…To produce low-frequency burst waves with desired acoustic intensity and directivity, several hundreds of Tonpilz transducers are employed as source elements for a large-aperture array projector [4]. However, bulky and heavy Tonpilz transducers are not suitable for the array elements due to the payload limit of the array platform [5]. To alleviate this issue, a small-sized single projector design with a resonance mode within, for example, a low-frequency band is required.…”