Limits of the resonance spectrum of tube arrays immersed in a fluid

Abstract

The resonance frequency spectrum of an elastic tube array placed in a still fluid is spread over a relatively wide interval. This interval depends on the added mass matrix of the bundle. This matrix reflects the mechanical interaction of tubes through the fluid. When the bundle is practically infinite (i.e. with a large number of tubes), the added mass matrix can be expressed by the "Bloch wave" decomposition, valid for infinite periodic structures. That allows to show that the resonance spectrum of the fluid-bundle system is continuous and therefore spread over an interval. It then becomes easy to compute the limits of this interval. Both cases of incompressible and compressible fluids are investigated.