Keywords: reduced model, fluid-structure interaction, non-linear vibration, vibro-acoustic coupling, temporal integration.

This paper presents a modal reduction method for a fluid-structure interaction problem including localized non-linearities. Research usually has been focused on the linear coupling problem, but non-linear effects appear in many industrial applications. A study of a structure presenting non-linear behaviour arising from the large displacements imposed, coupled with a fluid presenting linear behaviour is carried out. The description of the variation formulation based on structural displacement and fluid pressure variation is first presented. A matrix equation using the finite element method is written in the time domain. Using an uncoupled modal basis for modal reduction leads to an inadequate model compared to the original one. Coupling is considered by including residues issued from the fluid response due to the structure. Non-linear information is added to the Ritz basis by inserting the static response of the structure due to unit forces applied on the localized nonlinear degrees of freedom. A singular value decomposition of the basis is finally used to ensure proper conditioning of the problem. In the time domain, the problem is solved by using the implicit Newmark algorithm coupled with a Newton-Raphson correction to take into account the nonlinear effects. A numerical application based on an exhaust is presented. The comparisons between the full and reduced models show the necessity to include residue terms in the Ritz basis to ensure fast convergence.

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