Kaplunov, J and Nobili, A (2016) Multi-parametric analysis of strongly inhomogeneous periodic waveguides with internal cutoff frequencies. Mathematical Methods in the Applied Sciences, 40 (9). pp. 3381-3392.

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Abstract

In this paper, we consider periodic waveguides in the shape of a inhomogeneous string or beam partially supported by a uniform elastic Winkler foundation. A multi‐parametric analysis is developed to take into account the presence of internal cutoff frequencies and strong contrast of the problem parameters. This leads to asymptotic conditions supporting non‐typical quasi‐static uniform or, possibly, linear microscale displacement variations over the high‐frequency domain. Macroscale governing equations are derived within the framework of the Floquet–Bloch theory as well as using a high‐frequency‐type homogenization procedure adjusted to a string with variable parameters. It is found that, for the string problem, the associated macroscale equation is the same as that applying to a string resting on a Winkler foundation. Remarkably, for the beam problem, the macroscale behavior is governed by the same equation as for a beam supported by a two‐parameter Pasternak foundation.

Item Type: Article
Additional Information: This is the peer reviewed version of the following article: Kaplunov, J. & Nobili, A., 2016. Multi-parametric analysis of strongly inhomogeneous periodic waveguideswith internal cutoff frequencies. Mathematical Methods in the Applied Sciences, p.n/a–n/a. which has been published in final form at at: http://dx.doi.org/10.1002/mma.3900 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
Uncontrolled Keywords: periodic waveguide, cutoff frequency, homogenization, contrast, high-frequency
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Depositing User: Symplectic
Date Deposited: 02 Mar 2016 12:28
Last Modified: 15 Apr 2019 11:39
URI: http://eprints.keele.ac.uk/id/eprint/1513

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