A multi-scale model order reduction scheme for transient modelling of periodic structures. (13th October 2021) - Droz, Christophe; Boukadia, Régis; Desmet, Wim
Abstract: In this paper, a Floquet Model Order Reduction (MOR) method is proposed for the modelling of finite periodic structures subjected to harmonic or transient loads. This Floquet MOR generates frequency-independent projection matrices of the full-scale structure using a Floquet expansion of the local state-vectors computed on a single unit-cell with the Forced Wave Finite Element framework. This two-step MOR method can handle large multi-scale waveguides regardless of the scale and the number of unit-cells. A comparison with a standard sub-structuring approach based on unit-cell wave-mode reduction demonstrates that Floquet MOR is able to create reduced models of finite periodic structures with an unequalled computational efficiency. The method's ability to produce small and accurate models suitable for time-domain simulations presents a high potential for virtual sensing, real-time Structural Health Monitoring (SHM) and digital twins for large periodic structures and metamaterials. Highlights: We introduce an original MOR technique for transient simulations in periodic media. The reduced model of the overall structure is built from a single unit-cell analysis. The numerical framework is based on WFEM and exploits a POD-like Floquet expansion. The MOR handles complex waveguiding effects and is validated on a metamaterial model.