Analysis of the scattering of a plane acoustic wave by a doubly periodic structure using the finite‐element method

In an attempt to design low‐frequency nonreflecting or nontransmitting coatings for underwater applications, many new heterogeneous multilayer structures have been studied in recent years. In the general case, each layer is homogeneous and more or less complex models can be built using a standard transfer‐matrix approach. However, in some cases, one or several constitutive layers contain doubly periodic inclusions, such as spherical or cylindrical cavities, used to enhance energy absorption via resonance effects. Then, the modeling requires a larger effort to take account of this periodicity and of the actual displacement field inside each elementary cell. To do this, a finite‐element approach has been set up, using the ATILA code and following the method already developed to analyze wave scattering by compliant tube gratings [A. C. Hennion et al., J. Acoust. Soc. Am. 87, 1861–1870 (1990)]. Within this approach, only the unit cell of the structure, including a small part of the surrounding fluid domain, h...