BLOCH-WAVE HOMOGENIZATION FOR A SPECTRAL PROBLEM IN FLUID-SOLID STRUCTURES

This paper is concerned with the study of the vibrations of a coupled fluid-solid periodic structure. As the period goes to zero, an asympto tic analysis of the spectrum (i.e., the set of eigenfrequencies) is pe rformed with the help of a new method, the so-called Bloch-wave homoge nization method (which is a blend of two-scale convergence and Bloch-w ave decomposition). The limit spectrum is made of three parts: the mac roscopic or homogenized spectrum, the microscopic or Bloch spectrum, a nd the boundary-layer spectrum. The two first parts are completely cha racterized: The homogenized and the Bloch spectra are purely essential , and have a band structure. The boundary-layer spectrum is shown to b e empty in the special case of periodic boundary condition.