A spectral problem arising in fluid-solid structures

Abstract

In this paper, we study a simplified model that describes the eigenfrequencies and eigenmotions of a periodic tube bundle immersed in an incompressible, perfect fluid. This model involves Laplace equations and a nonlocal boundary condition. The eigenvalues of the problem appear in this nonlocal condition. In practice we are interested in the case where one has very many tubes. Our goal in this article is to study the asymptotic behaviour of the spectrum of these problems as the number of tubes goes to infinity. We do this in terms of the convergance of the spectral families associated with these problems.