A wave-based numerical approach for fast analysis of the dynamic response of periodic structures with local perturbations

Jean-Mathieu Mencik (1) , Denis Duhamel (2)

1 LMR - Laboratoire de Mécanique et de Rhéologie
2 navier umr 8205 - Laboratoire Navier

A wave finite element (WFE) based approach is proposed to analyze the dynamic behavior of finite-length periodic structures which are made up of identical substructures but also contain several substructures whose material and geometric characteristics are slightly perturbed. Within the WFE framework, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two unperturbed substructures, and considering perturbed parts which are composed of perturbed substructures 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 two perturbed substructures which can be randomly located. The relevance of the WFE-based approach is clearly established in comparison with the FE method, in terms of accuracy and computational saving. Additional simulations are made to examine the feasibility to improve the robustness of periodic structures to the occurrence of a arbitrary slight perturbation, by artificially adding several " controlled " perturbed substructures.

Domaines: Matériaux et structures en mécanique [physics.class-ph]

Jean-Mathieu Mencik, Denis Duhamel. A wave-based numerical approach for fast analysis of the dynamic response of periodic structures with local perturbations. ISMA 2016, Sep 2016, Leuven, Belgium. ⟨hal-01696145⟩