A wave-based model reduction technique for the description of the dynamic behavior of periodic structures involving arbitrary-shaped substructures and large-sized finite element models

International audienceThe wave finite element (WFE) method is investigated to describe the dynamic behavior of periodic structures like those composed of arbitrary-shaped substruc-tures along a certain straight direction. Emphasis is placed on the analysis of non-academic substructures that are described by means of large-sized finite element (FE) models. 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. An error indicator is also proposed to determine in an a priori process the number of those wave modes that need to be considered. Their computation hence follows by considering the Lanczos method, which can be achieved in a very fast way. Numerical experiments are carried out to highlight the relevance of the proposed reduction technique. 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