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Article Dans Une Revue Finite Elements in Analysis and Design Année : 2016

A wave finite element-based approach for the modeling of periodic structures with local perturbations

J.-M. Mencik
Denis Duhamel

Résumé

The wave finite element (WFE) method is investigated to describe the dynamic behavior of finite-length periodic structures with local perturbations. The structures under concern are made up of identical substructures along a certain straight direction, but also contain several perturbed substructures whose material and geometric characteristics undergo arbitrary slight variations. Time-harmonic elasticity is considered. Emphasis is on the development of a numerical tool which is fast and accurate for computing the related forced responses. To achieve this task, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two unperturbed sub-structures, and considering perturbed parts which are composed of perturbed sub-structures surrounded by two unperturbed ones. In doing so, a few wave modes are only required for modeling the central periodic structure, outside the perturbed parts. For forced response computation purpose, a reduced wave-based matrix formulation is established which follows from the consideration of transfer matrices between the right and left sides of the perturbed parts. Numerical experiments are carried out on a periodic 2D structure with one or two perturbed substructures to validate the proposed approach in comparison with the finite element (FE) method. Also, Monte Carlo (MC) simulations are performed with a view to assessing the sensitivity of a purely periodic structure to the occurrence of arbitrarily located perturbations. A strategy is finally proposed for improving the robustness of periodic structures. It involves artificially adding several " controlled " perturbations for lowering the sensitivity of the dynamic response to the occurrence of other uncontrolled perturbations.
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Dates et versions

hal-01695311 , version 1 (29-01-2018)

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J.-M. Mencik, Denis Duhamel. A wave finite element-based approach for the modeling of periodic structures with local perturbations. Finite Elements in Analysis and Design, 2016, 121, pp.40 - 51. ⟨10.1016/j.finel.2016.07.010⟩. ⟨hal-01695311⟩
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