State-space Bloch mode synthesis for fast band-structure calculations of non-classically damped phononic materials

Bloch mode synthesis (BMS) techniques enable efficient band-structure calculations of periodic media by forming reduced order models of the unit cell. Rooted in the framework of the Craig-Bampton component mode synthesis methodology, these techniques decompose the unit cell into interior and boundary degrees-of-freedom that are nominally described, respectively, by sets of normal modes and constraint modes. In this paper, we generalize the BMS approach by state-space transformation to extend its applicability to generally damped periodic materials that violate the Caughey-O'Kelly condition for classical damping. In non-classically damped periodic models, the fixed-interface eigenvalue problem may, in general, produce a mixture of underdamped and overdamped modes. We examine two mode-selection schemes for the reduced-order model and demonstrate the underlying accuracy-efficiency trade-offs when qualitatively distinct mixtures of underdamped and overdamped modes are incorporated. The proposed approach provides a highly effective computational tool for analysis of large models of phononic crystals and acoustic/elastic metamaterials with complex damping properties.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper generalizes the Bloch mode synthesis (BMS) approach using state-space transformation to extend its applicability to generally damped periodic materials. The study examines mode-selection schemes for non-classically damped periodic models and demonstrates the trade-offs between accuracy and efficiency.