Floquet Theory for Discontinuously Supported Waveguides | Zendy

Andrea Sorzia | Zendy

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Floquet Theory for Discontinuously Supported Waveguides

Author(s) -

Andrea Sorzia

Publication year - 2016

Publication title -

modelling and simulation in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 20

eISSN - 1687-5591

pISSN - 1687-5605

DOI - 10.1155/2016/2651953

Subject(s) - floquet theory , dispersion (optics) , mathematical analysis , ode , waveguide , stability (learning theory) , mathematics , string (physics) , physics , classical mechanics , optics , quantum mechanics , mathematical physics , nonlinear system , machine learning , computer science

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

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