Development of a new vibroacoustic superelement for heavy-fluid cavities

Abstract

We propose a Reduced Order Model (ROM) of heavy-fluid cavities with the objective to build a superelement in a finite element substructuring context. We consider the non-symmetric displacement-pressure finite element formulation. While there are numerous fluid-structure ROM in the literature, few are generalized to superelements. Typical vibroacoustic substructuring methods involve modal synthesis using uncoupled rigid-wall fluid modes and in vacuo structure modes. Vibroacoustic domains are composed of a structural domain and a fluid domain coupled on a fluid-structure boundary. Each domain can be modeled by symmetric monophysics formulations. Only the fluid-structure boundary requires a non-symmetric multiphysics formulation. Being defined on a submanifold, this subproblem is typically significantly smaller than the other subproblems. We propose to condense the uncoupled subdomains onto the fluid-structure boundary and use a Petrov-Galerkin procedure to obtain a reduced order representation of this loaded boundary. The captured boundary dynamics is then propagated to each uncoupled subdomain. Galerkin procedures are also applied to the uncoupled subproblems to increase the reduction bases. At the end, a Petrov-Galerkin procedure is applied to the full order model to build the superelement. The proposed superelement generation strategy is used to study an industrial water tank in a seismic analysis context. Results show a significant improvement over typical uncoupled superelements at the same reduction basis size. While the uncoupled superelements cannot describe the dynamics of the model beyond the weakly-coupled sloshing regime, the proposed superelement accurately captures the strongly-coupled dynamics in the studied frequency bandwidth.