A novel model-order reduction method for hydroelastic periodic structures with strong fluid–structure interaction and sloshing within the Wave Finite Element Method framework

Periodic structures have gained considerable attention due to the wide range of functionalities they can offer for wave manipulation. Their study often relies on wave propagation analyses, including the computation of band diagrams, wavemodes, harmonic forced responses, and so forth. Thus, the need for efficient modeling techniques has become crucial to understand their dynamic behavior at an affordable computational cost. In particular, the Wave-based Finite Element Method (WFEM) has emerged as a prominent modeling strategy for the analysis of periodic media, as it enables numerical simulations to be performed without the need to mesh the complete lattice; that is, only a single unit cell of the assembly is analyzed within the WFEM. Although the WFEM fundamentally offers great advantages compared with other simulation techniques, such as the FEM, the analysis of periodic structures by the WFEM can be challenging when unit cells possess many internal and boundary degrees of freedom (DoFs). A large number of internal DoFs in a unit cell causes the dynamic condensation of (internal) DoFs within the WFEM to become very slow or even impossible, while many boundary DoFs increase the complexity of obtaining the so-called wave modes due to the numerous evanescent modes. Model-order reduction has therefore become a key solution for improving the WFEM performance, enabling its application to more complex problems, including those encountered in industrial applications and/or those involving analyses at higher frequencies, which typically require finer meshes and consequently models with a larger number of DoFs. This paper accordingly reports recent advances in the modeling of hydroelastic periodic structures with strong fluid--structure interaction and sloshing, employing reduced-order unit cell models combined with the WFEM. Numerical simulations demonstrate that accurate reduced-order unit cell models can be derived using the proposed model reduction strategy, effectively replacing large-size finite element models, and enabling time-efficient simulations by the WFEM.