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

This paper introduces a new reduction scheme for the Wave/Finite Element (WFE) Framework, able to efficiently compute forced response and complex dispersion curves of periodic structures modelled using large-sized finite element models (FEM). The method involves a projection of the direct Bloch problem on a subset of propagative and evanescent wave solutions obtained using the inverse approach. These solutions are computed on a reduced number of k-space samples derived from a single resolution of the direct Bloch problem, where component modes are used to perform dynamic condensation of the unit-cell. Then, a singular value decomposition is performed on the collected eigenvectors, to create a truncated wave basis ensuring the method's robustness within the selected bandwidth. It provides a well-conditioned reduced model for Direct λ(ω) Bloch wave computation, which is then compatible with frequency-dependent material properties, vibroacoustic transmission/reflection problems as well as for near or far field analyses in finite structures subjected to dynamic loading. In a first example, the method is used to compute with high frequency resolution the dispersion curves and forced response of a hollow beam exhibiting complex vibroacoustic behaviour. The second application explores the propagation and localization of guided resonances in an orthogonally stiffened plate. The significant reduction factors (over 500) obtained enable wave propagation analyses in complex FE designs such as stop-band phononic crystals or locally resonant metamaterials with almost negligible computational effort. Furthermore, the proposed method can be used in a mid-frequency context, to describe attenuation or edge modes behaviours occurring inside the stop-bands, as evanescent solutions are also computed in this direct approach.

Publication year:2018

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IOF-keylabel:yes

BOF-publication weight:2

CSS-citation score:2

Authors:International

Authors from:Higher Education

Accessibility:Open