Journal
JOURNAL OF SOUND AND VIBRATION
Volume 442, Issue -, Pages 624-644Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jsv.2018.10.045
Keywords
Quasi-periodic; Band gap; Vibration; Beam lattice; Dispersion relation
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Funding
- CNRS, France through METAMORPH PEPS project
- ANR France [ANR-16-CE30-0007-01]
- Agence Nationale de la Recherche (ANR) [ANR-16-CE30-0007] Funding Source: Agence Nationale de la Recherche (ANR)
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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. (C) 2018 Elsevier Ltd. All rights reserved.
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