Floquet Theory for Discontinuously Supported Waveguides
We apply Floquet theory of periodic coefficient second-order ODEs to an elastic waveguide. The waveguide is modeled as a uniform elastic string periodically supported by a discontinuous Winkler elastic foundation and, as a result, a Hill equation is found. The fundamental solutions, the stability re...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Modelling and Simulation in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2016/2651953 |
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| author | A. Sorzia |
| author_facet | A. Sorzia |
| author_sort | A. Sorzia |
| collection | DOAJ |
| description | We apply Floquet theory of periodic coefficient second-order ODEs to an elastic waveguide. The waveguide is modeled as a uniform elastic string periodically supported by a discontinuous Winkler elastic foundation and, as a result, a Hill equation is found. The fundamental solutions, the stability regions, and the dispersion curves are determined and then plotted. An asymptotic approximation to the dispersion curve is also given. It is further shown that the end points of the band gap structure correspond to periodic and semiperiodic solutions of the Hill equation. |
| format | Article |
| id | doaj-art-9dc2eaefddbf4d4d8f732780a05a3bad |
| institution | Kabale University |
| issn | 1687-5591 1687-5605 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Modelling and Simulation in Engineering |
| spelling | doaj-art-9dc2eaefddbf4d4d8f732780a05a3bad2025-02-03T01:22:47ZengWileyModelling and Simulation in Engineering1687-55911687-56052016-01-01201610.1155/2016/26519532651953Floquet Theory for Discontinuously Supported WaveguidesA. Sorzia0Dipartimento di Scienze e Metodi dell’Ingegneria (DISMI), Universitá degli Studi di Modena e Reggio Emilia, Via G. Amendola 2, 42122 Reggio Emilia, ItalyWe apply Floquet theory of periodic coefficient second-order ODEs to an elastic waveguide. The waveguide is modeled as a uniform elastic string periodically supported by a discontinuous Winkler elastic foundation and, as a result, a Hill equation is found. The fundamental solutions, the stability regions, and the dispersion curves are determined and then plotted. An asymptotic approximation to the dispersion curve is also given. It is further shown that the end points of the band gap structure correspond to periodic and semiperiodic solutions of the Hill equation.http://dx.doi.org/10.1155/2016/2651953 |
| spellingShingle | A. Sorzia Floquet Theory for Discontinuously Supported Waveguides Modelling and Simulation in Engineering |
| title | Floquet Theory for Discontinuously Supported Waveguides |
| title_full | Floquet Theory for Discontinuously Supported Waveguides |
| title_fullStr | Floquet Theory for Discontinuously Supported Waveguides |
| title_full_unstemmed | Floquet Theory for Discontinuously Supported Waveguides |
| title_short | Floquet Theory for Discontinuously Supported Waveguides |
| title_sort | floquet theory for discontinuously supported waveguides |
| url | http://dx.doi.org/10.1155/2016/2651953 |
| work_keys_str_mv | AT asorzia floquettheoryfordiscontinuouslysupportedwaveguides |