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Modelling and Simulation in Engineering
Volume 2016, Article ID 2651953, 7 pages
Research Article

Floquet Theory for Discontinuously Supported Waveguides

Dipartimento di Scienze e Metodi dell’Ingegneria (DISMI), Universitá degli Studi di Modena e Reggio Emilia, Via G. Amendola 2, 42122 Reggio Emilia, Italy

Received 24 December 2015; Accepted 5 May 2016

Academic Editor: Julius Kaplunov

Copyright © 2016 A. Sorzia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.