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

Area of Science:

• Acoustics and Signal Processing
• Array Antenna Design
• Computational Electromagnetics

Background:

• Traditional geodesic-faceted arrays (GFAs) use the icosahedron method, leading to nonuniform triangle geometries and design inefficiencies.
• Spherical arrays (SAs) offer high performance but can be element-intensive.
• A need exists for efficient GFA design methods that overcome geometric distortions and reduce element count.

Purpose of the Study:

• To introduce a novel analytical method for designing geodesic-faceted arrays (GFAs) with uniform triangles.
• To achieve beam performance equivalent to spherical arrays (SAs) with a reduced number of elements.
• To provide a faster, more resource-efficient, and flexible alternative to conventional GFA design methods.

Main Methods:

• Developed characteristic equations relating geodesic triangles to spherical platforms based on frequency and geometric parameters.
• Derived a directional factor to calculate the array's beam pattern.
• Synthesized a GFA design for an underwater sonar imaging system using an optimization process.
• Validated theoretical designs using finite element method (FEM) simulations.

Main Results:

• The novel GFA design achieved nearly equivalent performance to a typical SA.
• A 16.5% reduction in the number of array elements was observed for the GFA compared to the SA.
• FEM simulations showed high compliance with theoretical results for both GFA and SA.
• The proposed analytical method demonstrated faster computation and lower resource requirements than FEM.

Conclusions:

• The novel analytical method provides an efficient approach for designing uniform-triangle GFAs.
• This method offers significant element reduction while maintaining high beam performance, crucial for applications like sonar imaging.
• The approach is more flexible and computationally advantageous than traditional methods and FEM.