1. Introduction

In the nuclear industry, some structures consist of almost periodic networks of tubes bathed in fluids: « fuel » assemblies, steam generators,… To determine the vibratory behavior of such structures, the classical approach (each tube is modelled, the volume occupied by the fluid is meshed) is expensive and tedious and even impractical (in particular, development of a complicated mesh containing a large number of nodes). Since the structures studied are almost periodic, it seems interesting to use homogenization methods.

Homogenization techniques applied to a network of tubes bathed in a fluid have been developed several times already [bib1], [bib5], [bib4]. The models obtained differ in the hypotheses made about the fluid (compressibility, initial flow speed, viscosity). According to accepted hypotheses, the action of the fluid on the network of tubes corresponds to added mass (reduction in vibration frequencies compared to those determined in the absence of fluid), to added damping or even to added stiffness [bib5].

At the beginning, finite elements associated with two-dimensional models (network of flyweights bathed in a fluid) were developed [bib2]. To study three-dimensional problems (network of tubes), one solution is to project the movement onto the first mode of flexure of the beams [bib4]. Subsequently, three-dimensional finite elements were developed [bib3], [bib8].