A micropolar model for the analysis of dispersive waves in chiral mass-in-mass lattices
The possibility of obtaining band gap structures in chiral auxetic lattices is here considered and applied to the case of inertial locally resonant structures. These periodic materials are modelled as beam-lattices made up of a periodic array of rigid rings, each one connected to the others through...
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Gruppo Italiano Frattura
2014-07-01
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| Series: | Fracture and Structural Integrity |
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| Online Access: | https://www.fracturae.com/index.php/fis/article/view/1273 |
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| author | A. Bacigalupo L. Gambarotta |
| author_facet | A. Bacigalupo L. Gambarotta |
| author_sort | A. Bacigalupo |
| collection | DOAJ |
| description | The possibility of obtaining band gap structures in chiral auxetic lattices is here considered and applied to the case of inertial locally resonant structures. These periodic materials are modelled as beam-lattices made up of a periodic array of rigid rings, each one connected to the others through elastic slender ligaments. To obtain low-frequency stop bands, elastic circular resonating inclusions made up of masses located inside the rings and connected to them through an elastic surrounding interface are considered and modeled. The equations of motion are obtained for an equivalent homogenized micropolar continuum and the overall elastic moduli and the inertia terms are given for both the hexachiral and the tetrachiral lattice. The constitutive equation of the beam lattice given by the Authors [15] are then applied and a system of six equations of motion is obtained. The propagation of plane waves travelling along the direction of the lines connecting the ring centres of the lattice is analysed and the secular equation is derived, from which the dispersive functions may be obtained. |
| format | Article |
| id | doaj-art-36e18c752395420f983b77a65f89a031 |
| institution | Kabale University |
| issn | 1971-8993 |
| language | English |
| publishDate | 2014-07-01 |
| publisher | Gruppo Italiano Frattura |
| record_format | Article |
| series | Fracture and Structural Integrity |
| spelling | doaj-art-36e18c752395420f983b77a65f89a0312025-01-03T01:05:20ZengGruppo Italiano FratturaFracture and Structural Integrity1971-89932014-07-0182910.3221/IGF-ESIS.29.01A micropolar model for the analysis of dispersive waves in chiral mass-in-mass latticesA. BacigalupoL. GambarottaThe possibility of obtaining band gap structures in chiral auxetic lattices is here considered and applied to the case of inertial locally resonant structures. These periodic materials are modelled as beam-lattices made up of a periodic array of rigid rings, each one connected to the others through elastic slender ligaments. To obtain low-frequency stop bands, elastic circular resonating inclusions made up of masses located inside the rings and connected to them through an elastic surrounding interface are considered and modeled. The equations of motion are obtained for an equivalent homogenized micropolar continuum and the overall elastic moduli and the inertia terms are given for both the hexachiral and the tetrachiral lattice. The constitutive equation of the beam lattice given by the Authors [15] are then applied and a system of six equations of motion is obtained. The propagation of plane waves travelling along the direction of the lines connecting the ring centres of the lattice is analysed and the secular equation is derived, from which the dispersive functions may be obtained.https://www.fracturae.com/index.php/fis/article/view/1273Auxetic materials |
| spellingShingle | A. Bacigalupo L. Gambarotta A micropolar model for the analysis of dispersive waves in chiral mass-in-mass lattices Fracture and Structural Integrity Auxetic materials |
| title | A micropolar model for the analysis of dispersive waves in chiral mass-in-mass lattices |
| title_full | A micropolar model for the analysis of dispersive waves in chiral mass-in-mass lattices |
| title_fullStr | A micropolar model for the analysis of dispersive waves in chiral mass-in-mass lattices |
| title_full_unstemmed | A micropolar model for the analysis of dispersive waves in chiral mass-in-mass lattices |
| title_short | A micropolar model for the analysis of dispersive waves in chiral mass-in-mass lattices |
| title_sort | micropolar model for the analysis of dispersive waves in chiral mass in mass lattices |
| topic | Auxetic materials |
| url | https://www.fracturae.com/index.php/fis/article/view/1273 |
| work_keys_str_mv | AT abacigalupo amicropolarmodelfortheanalysisofdispersivewavesinchiralmassinmasslattices AT lgambarotta amicropolarmodelfortheanalysisofdispersivewavesinchiralmassinmasslattices AT abacigalupo micropolarmodelfortheanalysisofdispersivewavesinchiralmassinmasslattices AT lgambarotta micropolarmodelfortheanalysisofdispersivewavesinchiralmassinmasslattices |