Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates
The effect of high contrast on the multiscale behaviour of elastic laminates is studied. Mathematical modelling in this area is of significant interest for a variety of modern applications, including but not limited to advanced sandwich structures and photovoltaic panels. As an example, the antiplan...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/18/3905 |
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| author | Lenser A. Aghalovyan Lusine G. Ghulghazaryan Julius Kaplunov Danila Prikazchikov |
| author_facet | Lenser A. Aghalovyan Lusine G. Ghulghazaryan Julius Kaplunov Danila Prikazchikov |
| author_sort | Lenser A. Aghalovyan |
| collection | DOAJ |
| description | The effect of high contrast on the multiscale behaviour of elastic laminates is studied. Mathematical modelling in this area is of significant interest for a variety of modern applications, including but not limited to advanced sandwich structures and photovoltaic panels. As an example, the antiplane shear of a symmetric, three-layered plate is considered. The problem parameters expressing relative thickness, stiffness and density are assumed to be independent. The high contrast may generally support extra length and time scales corresponding to degenerated boundary layers and propagating long-wave low-frequency vibration modes. The main focus is on the relation between these two phenomena. The developed multiparametric approach demonstrates that those do not always appear simultaneously. The associated explicit estimates on contrast parameters are established. In addition, the recent asymptotic extension of the classical Saint-Venant’s principle is adapted for calculating the contribution of the degenerate boundary layer or long-wave low-frequency propagation mode. The peculiarity of the limiting absorption principle in application to layered media is also addressed. |
| first_indexed | 2024-03-10T22:30:16Z |
| format | Article |
| id | doaj.art-a9676590fcfb467cb953d3399134b317 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T22:30:16Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a9676590fcfb467cb953d3399134b3172023-11-19T11:49:13ZengMDPI AGMathematics2227-73902023-09-011118390510.3390/math11183905Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic LaminatesLenser A. Aghalovyan0Lusine G. Ghulghazaryan1Julius Kaplunov2Danila Prikazchikov3Institute of Mechanics, National Academy of Sciences of the Republic of Armenia, Yerevan 0019, ArmeniaInstitute of Mechanics, National Academy of Sciences of the Republic of Armenia, Yerevan 0019, ArmeniaSchool of Computer Science and Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UKSchool of Computer Science and Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UKThe effect of high contrast on the multiscale behaviour of elastic laminates is studied. Mathematical modelling in this area is of significant interest for a variety of modern applications, including but not limited to advanced sandwich structures and photovoltaic panels. As an example, the antiplane shear of a symmetric, three-layered plate is considered. The problem parameters expressing relative thickness, stiffness and density are assumed to be independent. The high contrast may generally support extra length and time scales corresponding to degenerated boundary layers and propagating long-wave low-frequency vibration modes. The main focus is on the relation between these two phenomena. The developed multiparametric approach demonstrates that those do not always appear simultaneously. The associated explicit estimates on contrast parameters are established. In addition, the recent asymptotic extension of the classical Saint-Venant’s principle is adapted for calculating the contribution of the degenerate boundary layer or long-wave low-frequency propagation mode. The peculiarity of the limiting absorption principle in application to layered media is also addressed.https://www.mdpi.com/2227-7390/11/18/3905laminatehigh contrastmultiparametricmultiscaleasymptoticSaint-Venant’s principle |
| spellingShingle | Lenser A. Aghalovyan Lusine G. Ghulghazaryan Julius Kaplunov Danila Prikazchikov Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates Mathematics laminate high contrast multiparametric multiscale asymptotic Saint-Venant’s principle |
| title | Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates |
| title_full | Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates |
| title_fullStr | Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates |
| title_full_unstemmed | Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates |
| title_short | Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates |
| title_sort | degenerated boundary layers and long wave low frequency motion in high contrast elastic laminates |
| topic | laminate high contrast multiparametric multiscale asymptotic Saint-Venant’s principle |
| url | https://www.mdpi.com/2227-7390/11/18/3905 |
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