Multi-Region Matrix Interpolation for Dynamic Analysis of Aperiodic Structures under Large Model Parameter Perturbations

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.