Data-driven identification of bandgaps in flexural metastructures using Component Mode Synthesis and FRF Based Substructuring

Abstract

Metastructures, characterized by their periodic unit cells, are known for their ability to block the propagation of elastic waves within specific frequency ranges, known as “bandgaps”. To estimate the wave propagation characteristics of these systems, two primary approaches are employed: physics-based methods and data-driven techniques. Physics-based methods depend on the material properties and geometry of the unit cells, while data-driven approaches utilize experimental data, such as steady-state dynamic response data.

This study assesses the effectiveness of data-driven techniques, particularly Component Mode Synthesis (CMS) and Frequency Response Function-Based Substructuring (FBS), in identifying bandgaps in metastructures composed of multiple unit cells. The focus is on metastructures consisting of 1D beams that exhibit flexural wave behavior. Within these structures, two significant challenges arise when using frequency response functions based on out-of-plane response data: the absence of rotational degrees of freedom (dofs) and the presence of rigid-body modes. Both factors critically impact the dispersion relationship and, by extension, the bandgap estimation. Traditionally, capturing rotational dynamics has been difficult due to limitations in direct experimental measurement, necessitating the inference of rotational dofs from translational measurements. Furthermore, rigid-body modes are estimated from experimental data. To overcome these challenges, we propose the estimation of rotational dofs by curve-fitting of translational dofs. In addition, this study explores a novel approach to the estimation of rigid body modes from the modal parameters acquired using the well-known Polymax algorithm. The discussed methodologies are also applied to derive dispersion relations for infinite metastructures.