Hierarchical band gaps in complex periodic systems
Complex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of periodic systems with very large unit cells can be predicted w...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-06-01
|
| Series: | Comptes Rendus. Mécanique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.249/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825205955413934080 |
|---|---|
| author | Dunckley, Lucas Davies, Bryn |
| author_facet | Dunckley, Lucas Davies, Bryn |
| author_sort | Dunckley, Lucas |
| collection | DOAJ |
| description | Complex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of periodic systems with very large unit cells can be predicted without numerical simulation. We study a class of difference equations with periodic coefficients and show that they inherit spectral gaps from their constituent elements. This result shows that if a frequency falls in a band gap for every constituent element then it must be in a band gap for the combined complex periodic structure. This theory and its instantaneous utility is demonstrated in a series of vibro-acoustic and mechanical examples. |
| format | Article |
| id | doaj-art-c19057ca30e84f1ba59a2cbff208b97e |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-c19057ca30e84f1ba59a2cbff208b97e2025-02-07T13:48:46ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342024-06-01352G114315610.5802/crmeca.24910.5802/crmeca.249Hierarchical band gaps in complex periodic systemsDunckley, Lucas0Davies, Bryn1https://orcid.org/0000-0001-8108-2316Department of Mathematics, Imperial College London, London, UKDepartment of Mathematics, Imperial College London, London, UKComplex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of periodic systems with very large unit cells can be predicted without numerical simulation. We study a class of difference equations with periodic coefficients and show that they inherit spectral gaps from their constituent elements. This result shows that if a frequency falls in a band gap for every constituent element then it must be in a band gap for the combined complex periodic structure. This theory and its instantaneous utility is demonstrated in a series of vibro-acoustic and mechanical examples.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.249/Transfer matrixBloch spectrumtracemetamaterialphononic crystal |
| spellingShingle | Dunckley, Lucas Davies, Bryn Hierarchical band gaps in complex periodic systems Comptes Rendus. Mécanique Transfer matrix Bloch spectrum trace metamaterial phononic crystal |
| title | Hierarchical band gaps in complex periodic systems |
| title_full | Hierarchical band gaps in complex periodic systems |
| title_fullStr | Hierarchical band gaps in complex periodic systems |
| title_full_unstemmed | Hierarchical band gaps in complex periodic systems |
| title_short | Hierarchical band gaps in complex periodic systems |
| title_sort | hierarchical band gaps in complex periodic systems |
| topic | Transfer matrix Bloch spectrum trace metamaterial phononic crystal |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.249/ |
| work_keys_str_mv | AT dunckleylucas hierarchicalbandgapsincomplexperiodicsystems AT daviesbryn hierarchicalbandgapsincomplexperiodicsystems |