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.

在本文中，提出了一种 Floquet 模型降阶 (MOR) 方法，用于对承受谐波或瞬态载荷的有限周期结构进行建模。该 Floquet MOR 使用强制波有限元框架在单个单元上计算的局部状态向量的 Floquet 扩展生成全尺寸结构的频率无关投影矩阵。无论单位单元的规模和数量如何，这种两步 MOR 方法都可以处理大型多尺度波导。与基于晶胞波模式简化的标准子结构化方法的比较表明，Floquet MOR 能够以无与伦比的计算效率创建有限周期结构的简化模型。