arXiv subjects

Romain Rumpler

Publications and source records attributed to Romain Rumpler.

3 recordsLinked to original sources

arXiv2026

Twisting Kelvin Cells for Enhanced Vibration Control

This work investigates the propagation of elastic waves in periodic Kelvin-cell chains, focusing on symmetry-breaking geometric modifications induced by twisting the cell's faces. By imposing such twists, the original lattice topology is preserved, while mirror symmetries are strategically broken through modifying a single geometric parameter, allowing wave characteristics to be adjusted without additional resonators or mass augmentation. The complex-valued Bloch-Floquet analysis reveals that twisting activates two distinct wave attenuation mechanisms: Bragg-type band gaps associated with periodicity-induced scattering, and polarization-dependent band gaps arising from longitudinal-torsional mode coupling and avoided crossings. To obtain qualitative and quantitative insight into these mechanisms, a simplified analytical model with coupled translational and rotational degrees of freedom is considered. The finite-element wave transmission calculations are experimentally validated on SLA-printed three-cell specimens, for which wave attenuation reaches up to 20 dB within the predicted band-gap frequencies. Note that high prediction accuracy requires accounting for viscoelastic material behavior, underscoring the importance of material behavior on the wave propagation characteristics. Overall, the findings show that modest geometric modifications to a classical Kelvin-cell lattice can enhance wave-filtering behavior, offering a tractable design strategy for vibration control in lightweight architected lattices.

physics.app-ph↗

arXiv2025

Consistent Parametric Model Order Reduction by Matrix Interpolation for Varying Underlying Meshes

Parametric model order reduction (pMOR) is a powerful tool for accelerating finite element (FE) simulations while maintaining parametric dependencies. For geometric parameters, pMOR by matrix interpolation is a well-suited approach because it does not require an affine representation of the parametric dependency, which is often not available for geometric parameters. However, the method requires that the underlying FE mesh has the same number of degrees of freedom and the same topology for all parameter configurations. This requirement can be difficult or even impossible to achieve for large parameter ranges or when automatic meshing is used. In this work, we propose a novel framework for pMOR by matrix interpolation for varying underlying meshes. The key idea is to understand the sampled reduced bases as continuous displacement fields that can be represented in different discretizations. By using mesh morphing and basis interpolation, the sampled reduced bases described in varying meshes can all be represented in terms of one reference mesh. This not only allows for performing pMOR by matrix interpolation, but also enables comparing the subspaces that the reduced bases span, which is important to detect strong changes that could lead to inconsistencies in the reduced operators. For mesh morphing, two strategies, namely morphing by spring analogy with elastic hardening and radial basis function morphing, were implemented and tested. Numerical experiments on a beam-shaped plate and a plate with a hole for one- and two-dimensional parameter spaces show that the proposed framework achieves high accuracy for both morphing methods and performs significantly better than two existing approaches for pMOR by matrix interpolation for varying underlying meshes.

math.NA↗

arXiv2024

Inconsistency Removal of Reduced Bases in Parametric Model Order Reduction by Matrix Interpolation using Adaptive Sampling and Clustering

Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are first sampled and then made consistent with each other by transforming the underlying reduced bases. Finally, the transformed reduced operators can be interpolated to predict reduced models for queried parameter points. However, the accuracy of the predicted reduced model strongly depends on the similarity of the sampled reduced bases. If the local reduced bases change significantly over the parameter space, inconsistencies are introduced in the training data for the matrix interpolation. These strong changes in the reduced bases can occur due to the model order reduction method used, a change of the system's dynamics with a change of the parameters, and mode switching and truncation. In this paper, individual approaches for removing these inconsistencies are extended and combined into one general framework to simultaneously treat multiple sources of inconsistency. For that, modal truncation is used for the reduction, an adaptive sampling of the parameter space is performed, and eventually, the parameter space is partitioned into regions in which all local reduced bases are consistent with each other. The proposed framework is applied to a cantilever Timoshenko beam and the Kelvin cell for one- to three-dimensional parameter spaces. Compared to the original version of parametric model order reduction by matrix interpolation and an existing method for inconsistency removal, the proposed framework leads to parametric reduced models with significantly smaller errors.

math.DS↗