Dispersion and localization in structured Rayleigh beams

A. Piccolroaz; A. B. Movchan

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arXiv · 1408.5020

Dispersion and localization in structured Rayleigh beams

A. Piccolroaz·A. B. Movchan

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Abstract

This paper brings a comparative analysis between dynamic models of couple-stress elastic materials and structured Rayleigh beams on a Winkler foundation. Although physical phenomena have different physical origins, the underlying equations appear to be similar, and hence mathematical models have a lot in common. In the present work, our main focus is on the analysis of dispersive waves, band-gaps and localized waveforms in structured Rayleigh beams. The Rayleigh beam theory includes the effects of rotational inertia which are neglected in the Euler--Bernoulli beam theory. This makes the approach applicable to higher frequency regimes. Special attention is given to waves in pre-stressed Rayleigh beams on elastic foundations.

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A. Piccolroaz, A. B. Movchan. 2014-08-21. Dispersion and localization in structured Rayleigh beams. https://arxiv.org/abs/1408.5020

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