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...

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Detalles Bibliográficos
Autores: González-Carbajal, Javier, Lemm, M., García Suárez, Joaquín
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
Descripción
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.