On the lowest-frequency bandgap of 1D phononic crystals
This manuscript puts forward and verifies an analytical approach for the design of phononic crystals that feature a bandgap at the lowest possible frequencies, in the sense of finding the optimal layer thicknesses for a given set of materials in a prescribed layering order. The mathematical formulat...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/166623 |
| Acceso en línea: | https://hdl.handle.net/11441/166623 https://doi.org/10.1016/j.euromechsol.2024.105466 |
| Access Level: | acceso abierto |
| Palabra clave: | Bandgap Laminate Low frequency Phononic crystal Wave propagation |
| Sumario: | This manuscript puts forward and verifies an analytical approach for the design of phononic crystals that feature a bandgap at the lowest possible frequencies, in the sense of finding the optimal layer thicknesses for a given set of materials in a prescribed layering order. The mathematical formulation rests upon the exact form of the half-trace function (half of the trace of the global transfer matrix) of the layered medium, which is directly connected to its bandgap structure. After showing that there is a tight relation between the frequency at which the first bandgap opens up and the curvature of the half-trace function at zero frequency, a new optimization strategy is proposed, based on the minimization of this curvature. Notably, the optimal solution is expressed as a closed-form equation and remains valid for any number of layers within the unit cell. We validate this analytical result by comparison with a numerically optimized design, finding remarkably good agreement between both solutions. |
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