Multi-parametric analysis of strongly inhomogeneous periodic waveguides with internal cutoff frequencies

Kaplunov

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.

Citation

Kaplunov. (2016). Multi-parametric analysis of strongly inhomogeneous periodic waveguides with internal cutoff frequencies. Mathematical Methods in the Applied Sciences, 3381-3392. https://doi.org/10.1002/mma.3900

• Acceptance Date: Feb 7, 2016
• Publication Date: Mar 7, 2016
• Journal: Mathematical Methods in the Applied Sciences
• Print ISSN: 0170-4214
• Publisher: Wiley
• Pages: 3381-3392
• DOI: https://doi.org/10.1002/mma.3900
• Keywords: periodic waveguide, cutoff frequency, homogenization, contrast, high-frequency
• Publisher URL: http://dx.doi.org/10.1002/mma.3900