Phononic Band Structure by Calculating Effective Parameters of One-Dimensional Metamaterials
Using a theory of homogenization that consists in the discretization of the inclusion of a binary phononic crystal in small volumes, in which the material parameters can be expanded in Fourier series, we have determined the dependence of the effective elastic parameters as a function of the frequenc...
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MDPI AG
2023-06-01
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| Series: | Crystals |
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| Online Access: | https://www.mdpi.com/2073-4352/13/6/931 |
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| author | Javier Flores Méndez Aurelio H. Heredia Jiménez Gustavo M. Minquiz A. Morales-Sánchez Mario Moreno José Alberto Luna López Francisco Severiano A. C. Piñón Reyes |
| author_facet | Javier Flores Méndez Aurelio H. Heredia Jiménez Gustavo M. Minquiz A. Morales-Sánchez Mario Moreno José Alberto Luna López Francisco Severiano A. C. Piñón Reyes |
| author_sort | Javier Flores Méndez |
| collection | DOAJ |
| description | Using a theory of homogenization that consists in the discretization of the inclusion of a binary phononic crystal in small volumes, in which the material parameters can be expanded in Fourier series, we have determined the dependence of the effective elastic parameters as a function of the frequency. In particular, the frequency dependence of all the elements that constitute the effective tensors of stiffness (moduli of elasticity) and density was analyzed for a 1D phononic crystal conformed of materials whose main characteristic is the high contrast between their elastic properties. In this dynamic case of homogenization, it was found that the effective parameters can reproduce the exact dispersion relations for the acoustic modes that propagate along the periodicity direction of the crystal. Particularly, in the second pass band (high-frequency branch) corresponding to the transverse vibrational modes, the homogenized elastic phononic crystal exhibits a metamaterial behavior because the effective <i>C</i><sub>44</sub>-component (shear modulus) and dynamic mass density were found to be both negative. It is noteworthy that the study derived from this homogenization technique can lead to design of double negative metamaterial systems for potential applications. |
| first_indexed | 2024-03-11T02:35:27Z |
| format | Article |
| id | doaj.art-0a0a1ee9222e4b18a1e780ca45d90652 |
| institution | Directory Open Access Journal |
| issn | 2073-4352 |
| language | English |
| last_indexed | 2024-03-11T02:35:27Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj.art-0a0a1ee9222e4b18a1e780ca45d906522023-11-18T09:56:44ZengMDPI AGCrystals2073-43522023-06-0113693110.3390/cryst13060931Phononic Band Structure by Calculating Effective Parameters of One-Dimensional MetamaterialsJavier Flores Méndez0Aurelio H. Heredia Jiménez1Gustavo M. Minquiz2A. Morales-Sánchez3Mario Moreno4José Alberto Luna López5Francisco Severiano6A. C. Piñón Reyes7Tecnológico Nacional de México/I.T. Puebla, Av. Tecnológico No. 420, Maravillas, Puebla 72220, MexicoFacultad de Electrónica—Universidad Popular Autónoma del Estado de Puebla, 21 sur No. 1103, Barrio de Santiago, Puebla 72410, MexicoTecnológico Nacional de México/I.T. Puebla, Av. Tecnológico No. 420, Maravillas, Puebla 72220, MexicoInstituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro No. 1, Sta. Ma. Tonantzintla, Puebla 72840, MexicoInstituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro No. 1, Sta. Ma. Tonantzintla, Puebla 72840, MexicoÁrea de Ingeniería—Benemérita Universidad Autónoma de Puebla, Ciudad Universitaria, Blvd. Valsequillo y Esquina, Av. San Claudio s/n, Col. San Manuel, Puebla 72570, MexicoInstituto Politécnico Nacional—Centro de Investigación en Biotecnología Aplicada Unidad Tlaxcala, Carretera a Santa Inés Tecuexcomac, a 1.5 km, Ex-Hacienda San Juan Molino, Tlaxcala 90700, MexicoTecnológico Nacional de México/I.T. Puebla, Av. Tecnológico No. 420, Maravillas, Puebla 72220, MexicoUsing a theory of homogenization that consists in the discretization of the inclusion of a binary phononic crystal in small volumes, in which the material parameters can be expanded in Fourier series, we have determined the dependence of the effective elastic parameters as a function of the frequency. In particular, the frequency dependence of all the elements that constitute the effective tensors of stiffness (moduli of elasticity) and density was analyzed for a 1D phononic crystal conformed of materials whose main characteristic is the high contrast between their elastic properties. In this dynamic case of homogenization, it was found that the effective parameters can reproduce the exact dispersion relations for the acoustic modes that propagate along the periodicity direction of the crystal. Particularly, in the second pass band (high-frequency branch) corresponding to the transverse vibrational modes, the homogenized elastic phononic crystal exhibits a metamaterial behavior because the effective <i>C</i><sub>44</sub>-component (shear modulus) and dynamic mass density were found to be both negative. It is noteworthy that the study derived from this homogenization technique can lead to design of double negative metamaterial systems for potential applications.https://www.mdpi.com/2073-4352/13/6/931phononic crystalshomogenization theorynegative effective parametersphononic bandmetamaterial |
| spellingShingle | Javier Flores Méndez Aurelio H. Heredia Jiménez Gustavo M. Minquiz A. Morales-Sánchez Mario Moreno José Alberto Luna López Francisco Severiano A. C. Piñón Reyes Phononic Band Structure by Calculating Effective Parameters of One-Dimensional Metamaterials Crystals phononic crystals homogenization theory negative effective parameters phononic band metamaterial |
| title | Phononic Band Structure by Calculating Effective Parameters of One-Dimensional Metamaterials |
| title_full | Phononic Band Structure by Calculating Effective Parameters of One-Dimensional Metamaterials |
| title_fullStr | Phononic Band Structure by Calculating Effective Parameters of One-Dimensional Metamaterials |
| title_full_unstemmed | Phononic Band Structure by Calculating Effective Parameters of One-Dimensional Metamaterials |
| title_short | Phononic Band Structure by Calculating Effective Parameters of One-Dimensional Metamaterials |
| title_sort | phononic band structure by calculating effective parameters of one dimensional metamaterials |
| topic | phononic crystals homogenization theory negative effective parameters phononic band metamaterial |
| url | https://www.mdpi.com/2073-4352/13/6/931 |
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