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A Bloch wave reduction scheme for ultrafast band diagram and dynamic response computation in periodic structures

By Regis F Boukadia, Christophe Droz, Mohamed N Ichchou and Wim Desmet

Abstract

© 2018 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 frequency-dependent 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 large-scaled periodic structures, complex phononic crystals designs or locally resonant metamaterials.status: publishe

Topics: Wave, Bloch theorem, Model reduction, Forced response, Evanescent waves, Periodic structures
Publisher: 'Elsevier BV'
Year: 2018
DOI identifier: 10.1016/j.finel.2018.05.007
OAI identifier: oai:lirias2repo.kuleuven.be:123456789/594278
Provided by: Lirias
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