This work introduces a surrogate-based model for efficiently estimating the frequency response of dynamic mechanical metamaterials, particularly when dealing with large parametric perturbations and aperiodic substructures. The research builds upon a previous matrix interpolation method applied on top of a Craig-Bampton modal reduction, allowing the variations of geometrical features without the need to remesh and recompute Finite Element matrices. This existing procedure has significant limitations since it requires a common modal projection, which inherently restricts the allowable perturbation size of the model parameters, thereby limiting the model parameter space where matrices can be effectively interpolated. The present work offers three contributions: (1) It provides structural dynamic insight into the restrictions imposed by the common modal projection, demonstrating that ill-conditioning can be controlled, (2) it proposes an efficient, sampling-based procedure to identify the non-regular boundaries of the usable region in the model parameter space, and (3) it enhances the surrogate model to accommodate larger model parameter perturbations by proposing a multi-region interpolation strategy. The efficacy of this proposed framework is verified through two illustrative examples. The first example, involving a unit cell with a square plate and circular core, validates the approach for a single well-conditioned projection region. The second example, using a beam-like structure with vibration attenuation bands, demonstrates the true advantage of the multi-region approach, where predictions from traditional Lagrange interpolation deviated significantly with increasing perturbations, while the proposed method maintained high accuracy across different perturbation levels.

翻译：本研究提出了一种基于代理模型的动态力学超材料频率响应高效估计方法，特别适用于处理大参数扰动和非周期子结构的情况。该研究在先前应用于Craig-Bampton模态缩聚的矩阵插值方法基础上进行拓展，允许几何特征变化而无需重新划分网格和重新计算有限元矩阵。现有方法存在显著局限性，因其要求采用共同的模态投影，这本质上限制了模型参数的允许扰动范围，从而制约了矩阵可有效插值的模型参数空间。本工作提供了三个贡献：(1) 从结构动力学角度揭示了共同模态投影所施加的限制，证明了病态条件可被控制；(2) 提出了一种高效的基于采样的方法，用于识别模型参数空间中可用区域的非规则边界；(3) 通过提出多区域插值策略，增强了代理模型以适应更大的模型参数扰动。通过两个示例验证了所提框架的有效性。第一个示例涉及具有方形板和圆形核心的晶胞，验证了该方法在单个良态投影区域的有效性。第二个示例采用具有振动衰减带的梁状结构，展示了多区域方法的真正优势：当传统拉格朗日插值法随着扰动增大而显著偏离时，所提方法在不同扰动水平下均保持了高精度。