Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals
The consideration of material losses in phononic crystals leads naturally to the introduction of complex valued eigenwavevectors or eigenfrequencies representing the attenuation of elastic waves in space or in time, respectively. Here, we propose a new technique to obtain phononic band structures wi...
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| Format: | Article |
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MDPI AG
2019-07-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/9/14/2825 |
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| author | Ting-Ting Wang Vincent Laude Muamer Kadic Yan-Feng Wang Yue-Sheng Wang |
| author_facet | Ting-Ting Wang Vincent Laude Muamer Kadic Yan-Feng Wang Yue-Sheng Wang |
| author_sort | Ting-Ting Wang |
| collection | DOAJ |
| description | The consideration of material losses in phononic crystals leads naturally to the introduction of complex valued eigenwavevectors or eigenfrequencies representing the attenuation of elastic waves in space or in time, respectively. Here, we propose a new technique to obtain phononic band structures with complex eigenfrequencies but real wavevectors, in the case of viscoelastic materials, whenever elastic losses are proportional to frequency. Complex-eigenfrequency band structures are obtained for a sonic crystal in air, and steel/epoxy and silicon/void phononic crystals, with realistic viscous losses taken into account. It is further found that the imaginary part of eigenfrequencies are well predicted by perturbation theory and are mostly independent of periodicity, i.e., they do not account for propagation losses but for temporal damping of Bloch waves. |
| first_indexed | 2024-12-10T17:35:03Z |
| format | Article |
| id | doaj.art-b34be076c58747cdaee0587d0148562f |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-12-10T17:35:03Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-b34be076c58747cdaee0587d0148562f2022-12-22T01:39:34ZengMDPI AGApplied Sciences2076-34172019-07-01914282510.3390/app9142825app9142825Complex-Eigenfrequency Band Structure of Viscoelastic Phononic CrystalsTing-Ting Wang0Vincent Laude1Muamer Kadic2Yan-Feng Wang3Yue-Sheng Wang4Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, ChinaInstitut FEMTO-ST, Université Bourgogne Franche-Comté, CNRS, 25030 Besançon, FranceInstitut FEMTO-ST, Université Bourgogne Franche-Comté, CNRS, 25030 Besançon, FranceInstitute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, ChinaInstitute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, ChinaThe consideration of material losses in phononic crystals leads naturally to the introduction of complex valued eigenwavevectors or eigenfrequencies representing the attenuation of elastic waves in space or in time, respectively. Here, we propose a new technique to obtain phononic band structures with complex eigenfrequencies but real wavevectors, in the case of viscoelastic materials, whenever elastic losses are proportional to frequency. Complex-eigenfrequency band structures are obtained for a sonic crystal in air, and steel/epoxy and silicon/void phononic crystals, with realistic viscous losses taken into account. It is further found that the imaginary part of eigenfrequencies are well predicted by perturbation theory and are mostly independent of periodicity, i.e., they do not account for propagation losses but for temporal damping of Bloch waves.https://www.mdpi.com/2076-3417/9/14/2825phononic crystalband structureviscoelasticitycomplex band structure |
| spellingShingle | Ting-Ting Wang Vincent Laude Muamer Kadic Yan-Feng Wang Yue-Sheng Wang Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals Applied Sciences phononic crystal band structure viscoelasticity complex band structure |
| title | Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals |
| title_full | Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals |
| title_fullStr | Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals |
| title_full_unstemmed | Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals |
| title_short | Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals |
| title_sort | complex eigenfrequency band structure of viscoelastic phononic crystals |
| topic | phononic crystal band structure viscoelasticity complex band structure |
| url | https://www.mdpi.com/2076-3417/9/14/2825 |
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