A wave-based reduction technique for the dynamic behavior of periodic structures

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

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

The wave finite element (WFE) method is investigated to describe the dynamic behavior of periodic structures like those composed of arbitrary-shaped substructures along a certain straight direction. A generalized eigenproblem based on the so-called S + S −1 transformation is proposed for accurately computing the wave modes which travel in right and left directions along those periodic structures. Besides, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two extra substructures. In doing so, a few wave modes are only required for modeling the central periodic structure. A comprehensive validation of the technique is performed on a 2D periodic structure. Also, its efficiency in terms of CPU time savings is highlighted regarding a 3D periodic structure that exhibits substructures with large-sized FE models.

Mots clés: Wave Finite Element Method; Periodic Structures; Model Reduction; Structural Dynamics

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

Denis Duhamel, Jean-Mathieu Mencik. A wave-based reduction technique for the dynamic behavior of periodic structures . COMPDYN 2015, May 2015, Hersonissos, Greece. ⟨hal-01266388⟩