Work

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

Year: 2018

Type: article

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 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. • Direct Bloch wave analysis is performed with several orders of magnitude reduction of the computational effort. • The method significantly extends the WFE Framework capabilities to handle large complex periodic waveguides. • The proposed algorithm is robust in regards with evanescent modes and easy to implement.

Source: Finite Elements in Analysis and Design

DOI: 10.1016/j.finel.2018.05.007

Authors: Régis F. Boukadia, Christophe Droz, Mohamed N. Ichchou, Wim Desmet

Institutions: École Centrale de Lyon, KU Leuven

Language: English

Topic: Acoustic Wave Phenomena Research

Subfield: Acoustics and Ultrasonics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990