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Vibrational properties of quasi-periodic beam structures

Abstract : Quasi-periodic structures have been widely studied, notably in the atomic vibration domain. In this paper a beam structure based on Octagonal quasi-periodic tiling is studied. We provide a complete description of its vibrational response, including the density of its vibrational states, a detailed description of its vibration modes, and the computation of the dynamical structure factor (spectral density of energy) for transverse and for longitudinal waves. It is shown that quasi-periodic structures exhibit localized low frequency vibration modes that are due to resonant vibrations of isolated patterns in the quasi-periodic structure, but in opposite, high-frequency modes are (non-trivially) extended. Moreover, the paper shows the possible existence of band gaps in the vibrational response of periodic and quasi-periodic beam lattices as a function of the ratio between the bending and the tensile stiffness of the beams.
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https://hal.archives-ouvertes.fr/hal-03360640
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Submitted on : Thursday, September 30, 2021 - 10:02:15 PM
Last modification on : Wednesday, November 3, 2021 - 5:05:26 AM

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Arthur Glacet, Anne Tanguy, Julien Réthoré. Vibrational properties of quasi-periodic beam structures. Journal of Sound and Vibration, Elsevier, 2019, ⟨10.1016/j.jsv.2018.10.045⟩. ⟨hal-03360640⟩

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