A Bloch wave reduction scheme for ultrafast band diagram and dynamic response computation in periodic structures
Abstract
A variety of Reduced-Order Modelling (ROM) techniques have been developed for the Wave/Finite Element (WFE) Framework. However most of these techniques are not compatible with dynamic response computation or frequencydependent problems. This paper introduces a new reduction strategy for the WFE method, enabling the computation of both the forced response and the complex dispersion curves of periodic structures modelled using large-sized finite element (FE) models. The method exploits the duality between Inverse and Direct Bloch formulations to build a reduced solution subspace, accounting for both propagating and evanescent behaviours, while ensuring high reduction factors. This reduction strategy therefore enables the resolution of a wider range of problems, including near/far field response computation in finite waveguides subjected to dynamic loadings, or vibroacoustic transmission/reflection problems. First, the method is used to compute dispersion curves and forced response in a duct. Then a large bi-stiffened structure is studied to evaluate the method's performances. The high frequency resolution provided by the proposed ROM allows us to explore a variety of propagation and guided resonances localization effects, hardly accessible otherwise. Furthermore, the considerable reduction factors enable fast wave dispersion analyses in largescaled periodic structures, complex phononic crystals designs or locally resonant metamaterials.
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BibTeX
@article{boukadia2026bloch,
title = {{A Bloch wave reduction scheme for ultrafast band diagram and dynamic response computation in periodic structures}},
author = {Régis F Boukadia and Christophe Droz and Mohamed N Ichchou and Wim Desmet},
journal = {Finite Elements in Analysis and Design},
year = {2026},
month = oct,
doi = {10.1016/j.finel.2018.05.007},
url = {https://hal.science/hal-03373014v2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Bloch wave reduction scheme for ultrafast band diagram and dynamic response computation in periodic structures
AU - Régis F Boukadia
AU - Christophe Droz
AU - Mohamed N Ichchou
AU - Wim Desmet
PY - 2026
DA - 2026/10/27
JO - Finite Elements in Analysis and Design
DO - 10.1016/j.finel.2018.05.007
UR - https://hal.science/hal-03373014v2
AB - A variety of Reduced-Order Modelling (ROM) techniques have been developed for the Wave/Finite Element (WFE) Framework. However most of these techniques are not compatible with dynamic response computation or frequencydependent problems. This paper introduces a new reduction strategy for the WFE method, enabling the computation of both the forced response and the complex dispersion curves of periodic structures modelled using large-sized finite element (FE) models. The method exploits the duality between Inverse and Direct Bloch formulations to build a reduced solution subspace, accounting for both propagating and evanescent behaviours, while ensuring high reduction factors. This reduction strategy therefore enables the resolution of a wider range of problems, including near/far field response computation in finite waveguides subjected to dynamic loadings, or vibroacoustic transmission/reflection problems. First, the method is used to compute dispersion curves and forced response in a duct. Then a large bi-stiffened structure is studied to evaluate the method's performances. The high frequency resolution provided by the proposed ROM allows us to explore a variety of propagation and guided resonances localization effects, hardly accessible otherwise. Furthermore, the considerable reduction factors enable fast wave dispersion analyses in largescaled periodic structures, complex phononic crystals designs or locally resonant metamaterials.
SN - 0168-874X
SN - 1872-6925
ER -