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

• The wave finite element method is used for modeling periodic structures.
• Structures are made up of arbitrary-shaped substructures having large-sized FE models.
• An efficient eigenproblem is proposed to compute the wave modes accurately.
• Fast computation of the wave modes is achieved using a model reduction technique.
• Large CPU time savings are obtained when computing the forced response of periodic structures.

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. 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−1S+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.