Vibroacoustic interface conditions between prestressed structures and moving fluids

Abstract

Many applications involve coupling between prestressed solids and fluids (possibly flowing). Typical problems might be given by vibroacoustics of fluid-filled pressurized cavities, wave propagation, dynamics and stability of pipes conveying fluids. The goal of this work is to investigate jump conditions that hold for small linear perturbations at any impermeable interfaces, slip or bonded, plane or not, between fluids and structures in the presence of initial flow and prestress. First, the mixed Eulerian-Lagrangian description is briefly recalled. It yields an interesting unification between existing formulations for inviscid fluids (Galbrun's equation) and solids (updated Lagrangian formulation). Based on conservative equations obtained from this description, interface conditions are derived in an elegant manner thanks to the concept of generalized functions in distribution theory. These conditions are written in terms of a curvilinear coordinate system attached to the interface. They are shown to coincide with a direct linearization of standard Eulerian jump conditions. General interface conditions for displacement, stress, heat flux and temperature are given. As an example, these conditions are applied to the analysis of elastoacoustic wave propagation inside an inviscid fluid-filled pressurized duct. The combined effects of slip, prestress and initial flow are briefly discussed.