Spectral asymptotics of the Helmholtz model in fluid-solid structures

A model representing the vibrations of a coupled fluid-solid structure is c onsidered. This structure consists of a tube bundle immersed in a slightly compressible fluid. Assuming periodic distribution of tubes, this article d escribes the asymptotic nature of the vibration frequencies when the number of tubes is large. Our investigation shows that classical homogenization o f the problem is not sufficient for this purpose. Indeed, our end result pr oves that the limit spectrum consists of three parts: the macro-part which comes from homogenization, the micro-part and the boundary layer part. The last two components are new. We describe in detail both macro- and micro-pa rts using the so-called Bloch wave homogenization method. Copyright (C) 199 9 John Wiley & Sons, Ltd.