 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| L. Cabras, A.B. Movchan, and A. Piccolroaz, "Floquet-Bloch Waves in Periodic Networks of Rayleigh Beams: Cellular System, Dispersion Degenerations, and Structured Connection Regions," Mech. Solids. 52 (5), 549-563 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
5 |
Pages |
549-563 |
| DOI |
10.3103/S0025654417050107 |
| Title |
Floquet-Bloch Waves in Periodic Networks of Rayleigh Beams: Cellular System, Dispersion Degenerations, and Structured Connection Regions |
| Author(s) |
L. Cabras (University of Trento, via Calepina 14, Trento, 38122 Italy)
A.B. Movchan (University of Liverpool, 765 Brownlow Hill, Liverpool, L69 7ZX United Kingdom, abm@liv.ac.uk)
A. Piccolroaz (University of Trento, via Calepina 14, Trento, 38122 Italy) |
| Abstract |
The paper is dedicated to Professor N. F. Morozov on the occasion of his 85th birthday. In the paper, we consider new dispersive properties of elastic flexural waves in periodic structures with rotational inertia. The structure is represented as a lattice with elementary bonds of Rayleigh-type beams. Although such beams in the semiclassical regime react as the classical Euler-Bernoulli beams, they exhibit new interesting characteristics as the dispersion frequency of flexural waves increases. Special attention is paid to degenerate cases related to the so-called Dirac cones on dispersion surfaces and to the directed anisotropy for the doubly periodic lattice. A comparative analysis accompanied by numerical simulation is carried out for the Floquet-Bloch waves propagating in periodic flexible lattices of different geometry. |
| Keywords |
periodic networks of elastic Rayleigh beams, rotational inertia, dispersing Floquet-Bloch waves |
| References |
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| 2. | N. F. Morozov and Yu. V. Petrov,
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| 9. | N. F. Morozov and P. E. Tovstik,
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| 10. | L. I. Slepyan,
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(Springer-Verlag, Berlin, 2002). |
| 11. | M. Ryvkin and L. I. Slepyan,
"Crack in a 2D Beam Lattice: Analytical Solutions for Two Bending Modes,"
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58 (6) 902-917 (2010). |
| 12. | D. Bigoni and A. B. Movchan,
"Statics and Dynamics of Structural Interfaces in Elasticity,"
Int. J. Solids Struct.
39, 4843-4865 (2002). |
| 13. | T. Antonakakis, R. V. Craster, and S. Guenneau,
"Homogenization for Elastic Photonic Crystals and Dynamic Anisotropy,"
J. Mech. Phys. Solids
71 84-96 (2014). |
| 14. | A. B. Movchan and L. I. Slepyan,
"Band gap Green's Functions and Localized Oscillations,"
Proc. Royal Soc. London. Ser. A: Math. Phys. Sci.
463 2709-2727 (2007). |
| 15. | A. Piccolroaz and A. B. Movchan,
"Dispersion and Localization in Structured Rayleigh Beams,"
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51, 4452-4461 (2014). |
| 16. | A. Piccolroaz, A. B. Movchan, and L. Cabras,
"Dispersion Degeneracies and Standing Modes in Flexural Waves Supported by Rayleigh Beam
Structures,"
Int. J. Solids Struct.
109, 152-165 (2017). |
| 17. | R. C. McPhedran, A. B. Movchan, N. V. Movchan, et al.,
"'Parabolic' Trapped Modes and Steered Dirac Cones in Platonic Crystals,"
Proc. Roy. Soc. London. Ser. A
471, 20140746 (2015). |
|
| Received |
03 March 2017 |
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