Abstract Summary
A method for the model order reduction of heavy-fluid cavities is proposed with the goal of building superelements in a finite element substructuring context. The non-symmetric displacement-pressure finite element formulation is considered. While there are numerous fluid-structure reduced order models in the literature for specific load cases, few are applicable to superelements which must be as unspecialized as possible. Typical vibroacoustic superelement methods include the widespread modal synthesis using uncoupled rigid-wall fluid modes and dry structure modes, sometimes considering the fluid added-mass effects. Vibroacoustic domains are composed of a structural domain and a fluid domain coupled on a fluid-structure boundary. By domain subdivision, the uncoupled structural and fluid subdomains are identified. The associated subproblems can be modeled by symmetric monophysics formulations. Only the fluid-structure subdomain at the intersection of the fluid and structural domains must be studied using a non-symmetric multiphysics formulation. Being defined on a submanifold, this coupled subproblem is typically significantly smaller than the uncoupled subproblems. It is proposed to reduce the uncoupled subdomains onto the coupling 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. This leads to left and right global reduction bases. The Petrov-Galerkin procedure is also applied to the uncoupled subproblems to increase the reduction bases. Particular considerations have to be made regarding the nullspace when a fluid free surface is present. To that extent, the nullspace is determined analytically. Following the well-established Hurty/Craig-Bampton method, any set of retained structural degrees of freedom can be chosen before the reduction procedure without loss of generality. The superelement is then built by projection of the full order model operators onto the left and right reduction bases. The proposed method is applied to the study of a large industrial water tank in a seismic analysis context. Results show a significant improvement over the typical model order reduction methods at the same reduction basis size. While the projection onto uncoupled bases cannot describe the model past the sloshing regime, the proposed method accurately captures the dynamics of the system in the bandwidth of interest for seismic analysis.
