## T. Harmonic Analysis of the Scattering of a Plane-Wave by a PeriodicElastic Structure (HAR7)

In this analysis, only a two-dimensional or three-dimensionalelementary cell of the elastic structure and a part of the fluid domain thatsurrounds it are meshed. The matrix equation is reduced to:

where the various stiffness, mass, and connectivity matriceshave been modified after the assembly phase to take into account the specificboundary conditions and where Yi is the normal derivative of the pressure field incident on the mesh boundary. The single or double periodicity of the mesh is taken into account by aspecific Bloch type phase relation between nodes separated by one mesh step. On the fluid mesh boundaries, the pressure field is matched to a homogeneous orevanescent plane-wave series expansion. It is possible to model structureswith fluid on both sides or only on the front side. Different fluids can beused on the front and the back sides.

The user specifies the frequency and the incidence angle ofthe incident wave as well as the symmetry planes of the elementary cell thatcorrespond to the Bloch condition (see Paragraph I.3.E.2). The code computesthe real and imaginary parts of the pressure and displacement fields as well asthe transmission and reflection coefficients.

The matrices are assembled and stored to file by columns. The phase relation between nodes separated by one mesh step as well as thecoupling with homogeneous and evanescent plane-waves on the mesh boundaries areincorporated into the matrices, which then become non-symmetrical. Gaussianalgorithms are used to solve the problem, in single or double precision. Theinternal losses of the materials can be taken into account.