Lorenzo Morini, Zafer Gökay Tetik, Gal Shmuel, Massimiliano Gei
{"title":"关于准晶体生成的结构棒的频谱普遍性和带隙优化。","authors":"Lorenzo Morini, Zafer Gökay Tetik, Gal Shmuel, Massimiliano Gei","doi":"10.1098/rsta.2019.0240","DOIUrl":null,"url":null,"abstract":"<p><p>The dynamical properties of periodic two-component phononic rods, whose elementary cells are generated adopting the Fibonacci substitution rules, are studied through the recently introduced method of the toroidal manifold. The method allows all band gaps and pass bands featuring the frequency spectrum to be represented in a compact form with a frequency-dependent flow line on the surface describing their ordered sequence. The flow lines on the torus can be either closed or open: in the former case, (i) the frequency spectrum is periodic and the elementary cell corresponds to a canonical configuration, (ii) the band gap density depends on the lengths of the two phases; in the latter, the flow lines cover ergodically the torus and the band gap density is independent of those lengths. It is then shown how the proposed compact description of the spectrum can be exploited (i) to find the widest band gap for a given configuration and (ii) to optimize the layout of the elementary cell in order to maximize the low-frequency band gap. The scaling property of the frequency spectrum, that is a distinctive feature of quasicrystalline-generated phononic media, is also confirmed by inspecting band-gap/pass-band regions on the torus for the elementary cells of different Fibonacci orders. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.</p>","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6894518/pdf/","citationCount":"0","resultStr":"{\"title\":\"On the universality of the frequency spectrum and band-gap optimization of quasicrystalline-generated structured rods.\",\"authors\":\"Lorenzo Morini, Zafer Gökay Tetik, Gal Shmuel, Massimiliano Gei\",\"doi\":\"10.1098/rsta.2019.0240\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The dynamical properties of periodic two-component phononic rods, whose elementary cells are generated adopting the Fibonacci substitution rules, are studied through the recently introduced method of the toroidal manifold. The method allows all band gaps and pass bands featuring the frequency spectrum to be represented in a compact form with a frequency-dependent flow line on the surface describing their ordered sequence. The flow lines on the torus can be either closed or open: in the former case, (i) the frequency spectrum is periodic and the elementary cell corresponds to a canonical configuration, (ii) the band gap density depends on the lengths of the two phases; in the latter, the flow lines cover ergodically the torus and the band gap density is independent of those lengths. It is then shown how the proposed compact description of the spectrum can be exploited (i) to find the widest band gap for a given configuration and (ii) to optimize the layout of the elementary cell in order to maximize the low-frequency band gap. The scaling property of the frequency spectrum, that is a distinctive feature of quasicrystalline-generated phononic media, is also confirmed by inspecting band-gap/pass-band regions on the torus for the elementary cells of different Fibonacci orders. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.</p>\",\"PeriodicalId\":20020,\"journal\":{\"name\":\"Philosophical Transactions of the Royal Society A\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6894518/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Philosophical Transactions of the Royal Society A\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rsta.2019.0240\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2019/11/25 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Philosophical Transactions of the Royal Society A","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rsta.2019.0240","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2019/11/25 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
On the universality of the frequency spectrum and band-gap optimization of quasicrystalline-generated structured rods.
The dynamical properties of periodic two-component phononic rods, whose elementary cells are generated adopting the Fibonacci substitution rules, are studied through the recently introduced method of the toroidal manifold. The method allows all band gaps and pass bands featuring the frequency spectrum to be represented in a compact form with a frequency-dependent flow line on the surface describing their ordered sequence. The flow lines on the torus can be either closed or open: in the former case, (i) the frequency spectrum is periodic and the elementary cell corresponds to a canonical configuration, (ii) the band gap density depends on the lengths of the two phases; in the latter, the flow lines cover ergodically the torus and the band gap density is independent of those lengths. It is then shown how the proposed compact description of the spectrum can be exploited (i) to find the widest band gap for a given configuration and (ii) to optimize the layout of the elementary cell in order to maximize the low-frequency band gap. The scaling property of the frequency spectrum, that is a distinctive feature of quasicrystalline-generated phononic media, is also confirmed by inspecting band-gap/pass-band regions on the torus for the elementary cells of different Fibonacci orders. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.