Application of the Finite Element Method to Analyze the Scattering of a Plane Acoustic Wave from Doubly Periodic Structures

Abstract

The scattering of a plane acoustic wave from immersed periodic structures has raised up a great deal of interest in underwater acoustics because they can be used as low frequency, wide bandwidth reflecting or absorbing baffles. These periodic structures are divided into two groups. The first one contains single periodic structures, such as single or double layered compliant tubes gratings, embedded or not in a viscoelastic layer. They are considered as reflecting baffles, in which the incident plane wave excites a resonance mode of the whole structure. The other group contains doubly periodic structures such as gradual tank lining or Alberich anechoic layers. They behave as a sound absorber, in which the incident plane acoustic wave excites a resonance mode of cylindrical or spherical inclusions, for instance. In order to explain their physical behavior and to help their design, several authors have built accurate mathematical models, which provided insertion loss values in nice agreement with measured values. Thus, Burke et al [1], Brigham et al [2], Duméry [3] and Audoly et al [4] have analyzed gratings of circular cylinders as well as of arbitrarily oriented, elliptically shaped compliant tubes, using a multiple scattering approach. From another point of view, Vovk et al [5], Radlinski et al [6] have used a waveguide approach to describe the behavior of tubes which have elongated rectangular section. Though powerful, all these methods require in every case a lot of specific algebraic developments, which restrict their use to a small number of given geometries. Moreover, they often rely upon simplifying assumptions for the structure or its displacement field, assumptions which rule out the resort to complex structures or materials. Thus, the use of the finite element method, with the help of ATILA code [7], to tackle these problems can strongly broaden the designer’s possibilities.

Associated to the CNRS, URA 253.