Finite-element analysis of planar sonar arrays by a coupled finite-element/modal-expansion method

Abstract

This paper presents the analysis of infinitely periodic planar sonar arrays by a coupled finite-element/modal-expansion method. Finite elements are used to model the region containing the sonar transducer. Here, the finite-element method solves the scalar Helmholtz equation for the acoustic potential. The finite-element method is well suited to solving the field behavior in the complex shape and heterogeneous material region of the sonar transducer. Coupled to the finite-element region is the semi-infinite region where the acoustic field behavior is periodic. In this region, the field behavior is defined by an infinite series Floquet modal expansion. The number of modes used in the Floquet expansion depends on the geometry and scan angle of the array. Typically, the number of modes is comprised of all the propagating modes plus 10 to 20 evanescent modes. This technique allows for the solution of array field behavior for any arbitrary scan angle. Being an infinite periodic analysis, however, limits the accuracy of the solution to the sonar elements in the middle of the array. This paper describes the use of this technique in two- and three-dimensional analysis and shows results in two dimensions.