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- Title
Elastic metamaterials with fractional-order resonators.
- Authors
Kaczmarek, Marcin B.; HosseinNia, S. Hassan
- Abstract
Elastic metamaterials incorporating locally resonating unit cells can create bandgap regions with lower vibration transmissibility at longer wavelengths than the lattice size and offer a promising solution for vibration isolation and attenuation. However, when resonators are applied to a finite host structure, not only the bandgap but also additional resonance peaks in its close vicinity are created. Increasing the damping of the resonator, which is a conventional approach for removing the undesired resonance peaks, results in shallowing of the bandgap region. To alleviate this problem, we introduce an elastic metamaterial with resonators of fractional order. We study a one-dimensional structure with lumped elements, which allows us to isolate the underlying phenomena from irrelevant system complexities. Through analysis of a single unit cell, we present the working principle of the metamaterial and the benefits it provides. We then derive the dispersion characteristics of an infinite structure. For a finite metastructure, we demonstrate that the use of fractional-order elements reduces undesired resonances accompanying the bandgap, without sacrificing its depth.
- Subjects
RESONATORS; UNIT cell; LUMPED elements; VIBRATION isolation; METAMATERIALS; RESONANCE
- Publication
Fractional Calculus & Applied Analysis, 2023, Vol 26, Issue 6, p2522
- ISSN
1311-0454
- Publication type
Article
- DOI
10.1007/s13540-023-00220-w