Designing a Geodesic Faceted Acoustical Volumetric Array Using a Novel Analytical Method

We present a novel analytical method as an efficient approach to design a geodesic-faceted array (GFA) for achieving a beam performance equivalent to that of a typical spherical array (SA). GFA is a triangle-based quasi-spherical configuration, which is conventionally created using the icosahedron method imitated from the geodesic dome roof construction process. In this conventional approach, the geodesic triangles have nonuniform geometries due to some distortions that occur during the random icosahedron division process. In this study, we took a paradigm shift from this approach and adopt a new technique to design a GFA that is based on uniform triangles. The characteristic equations that relate the geodesic triangle with a spherical platform were first developed as functions of the operating frequency and geometric parameters of the array. Then, the directional factor was derived to calculate the beam pattern associated with the array. A sample design of GFA for a given underwater sonar imaging system was synthesized through an optimization process. The GFA design was compared with that of a typical SA, and a reduction of 16.5% in the number of array elements was recorded in the GFA at a nearly equivalent performance. Both arrays were modeled, simulated, and analyzed using the finite element method (FEM) to validate the theoretical designs. Comparison of the results showed a high degree of compliance between the FEM and the theoretical method for both arrays. The proposed novel approach is faster and requires fewer computer resources than the FEM. Moreover, this approach is more flexible than the traditional icosahedron method in adjusting geometrical parameters in response to desired performance outputs.