Homogenization and Bloch wave method for fluid tube bundle interaction Original Research Article

The aim of this paper is to investigate the problem of the vibrations of large arrays of elastic rods immersed in a perfect incompressible fluid. The case of an infinite spatially periodic bundle is firstly considered leading to use the Bloch wave method in order to describe the resonance spectrum of the coupled system. When the bundle is contained in a bounded domain, the homogenization technique combined with the Bloch wave method allows to obtain the eigenspectrum which is formed of two eigenfrequencies (of infinite multiplicity), and of a continuous spectrum.