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

作者：Kaplunov J; Nobili A^*

来源：Mathematical Methods in the Applied Sciences, 2017, 40(9): 3381-3392.

DOI：10.1002/mma.3900

• periodic waveguide
• cutoff frequency
• homogenization
• contrast
• high frequency

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.

• 出版日期2017-6