Band Gaps of structures based on concrete-steel and concrete-molybdenum. Comparison between structures with square and hexagonal periodicities

Amrane AMINE, Abdelkader HASSEIN-BEY

Abstract


In this article, a study of the frequency dispersion curves of a periodic structure was made. The cell units of the base model are made of steel cylinders coated with a rubber layer embedded in a concrete thin mat. The results show the existence of three band gaps which means that we have no propagation waves. In second step, the steel core has been substituted with molybdenum. A noticeable shift towards the low frequencies has been achieved together with an improvement in the relative widths of the band gaps. In addition, a comparison of band gaps was made between a finites two-dimensional structure with square periodicity and hexagonal periodicity. The results showed that a square periodicity of a two-dimensional structure is more favourable for the field of civil engineering wich is necessary to be in a low frequencies.


Keywords


Seismic isolation; Bands gap: phononic cristals; Transmission

References


- J.W. Hu, Seismic analysis and parametric study of SDOF lead-rubber bearing (LRB) isolation systems with recentering shape memory alloy (SMA) bending bars. J. Mech. Sci. Technol. 30(7) (2016) 2987-2999. doi:10.1007/s12206-016-0608-5.

- P.-R. Wagner, V.K. Dertimanis, E.N. Chatzi, I.A. Antoniadis. Design of Metamaterials for Seismic Isolation. In: Pakzad, S., Juan, C. (eds) Dynamics of Civil Structures, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-29751-4_28.

- Bogdan Ungureanu, Younes Achaoui, Stéphane Brûlé, Richard Craster, Stefan Enoch, S. Guenneau, Exemples de métamateriaux sismiques existants, in 24ème Congrès Général de la Société Française de Physique Université Paris-Sud, Orsay (2017).

- M. Miniaci, A. Krushynska, F. Bosia, N.M. Pugno, Métamatériaux Mécaniques à Grande Echelle Pour Applications Sismiques, in 24ème Congrès Général de la Société Française de Physique Université Paris-Sud, Orsay (2017).

- R. Craster, A.Colombi, P. Roux, S. Guenneau, D. Colquitt, Y. Achaoui, S. Brule, Ultra-Low Broad Frequency Stop-Bands In Structured Elastic Media, in 24ème Congrès Général de la Société Française de Physique Université Paris-Sud, Orsay (2017).

- X.D. Nguyen. Contributions sur l’optimisation et l’analyse de l’isolation sismique des ponts dans les zones à sismicité modérée. PhD Thesis. École De Technologie Supérieure Université du Québec, Québec, 2021.

- M.S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, B. Djafari-Rouhani, Theory of acoustic band structure of periodic elastic composites. Physical Review B, 49(4) (1994) 2313-2322. doi:10.1103/PhysRevB.49.2313.

- M. Sigalas, M.S. Kushwaha, E.N. Economou, M. Kafesaki, I.E. Psarobas, W. Steurer, Classical vibrational modes in phononic lattices: theory and experiment. Zeitschrift für Kristallographie - Crystalline Materials, 220(9-10) (2005) 765-809. doi:10.1524/zkri.2005.220.9-10.765.

- A. Ganjoo, N. Yoshida, K. Shimakawa, Recent Research Developments in Applied Physics, ed. M. Kawasaki, N. Ashgritz and R. Anthony (Research Signpost, Trivandrurn, 2, 129, (1999).

- F.-C. Hsu, C.-I. Lee, J.-C. Hsu, T.-C. Huang, C.-H. Wang, P. Chang, Acoustic band gaps in phononic crystal strip waveguides. Applied Physics Letters, 96(5) (2010). doi:10.1063/1.3298643.

- L. Socié, S. Benchabane, L. Robert, A. Khelif, V. Laude, Surface acoustic wave guiding in a diffractionless high aspect ratio transducer. Applied Physics Letters, 102(11) (2013). doi:10.1063/1.4795939.

- A. Khelif, A. Choujaa, S. Benchabane, B. Djafari-Rouhani, V. Laude, Guiding and bending of acoustic waves in highly confined phononic crystal waveguides. Applied Physics Letters, 84(22) (2004) 4400-4402. doi:10.1063/1.1757642.

- S. Prabhukumar, R. Duraiwami, G.L. Chahine, Acoustic measurement of bubble size distributions: theory and experiments. Acoustical Society of America Journal, 236 (1996) 509-514.

- G.L. Chahine, K.M. Kalumuck, J.-Y. Cheng, G. Frederick, Validation of bubble distribution measurements of the ABS acoustic bubble spectrometer with high speed video photography, in Symp. Cav., CAV2001. (2001).

- Y. Lai, Z.-Q. Zhang, Large band gaps in elastic phononic crystals with air inclusions. Applied Physics Letters, 83(19) (2003) 3900-3902. doi:10.1063/1.1625998.

- J. Gao, X.-Y. Zou, J.-C. Cheng, B. Li, Band gaps of lower-order Lamb wave in thin plate with one-dimensional phononic crystal layer: Effect of substrate. Applied Physics Letters, 92(2) (2008). doi:10.1063/1.2834700.

- W. Xiao, G.W. Zeng, Y.S. Cheng, Flexural vibration band gaps in a thin plate containing a periodic array of hemmed discs. Applied Acoustics, 69(3) (2008) 255-261. doi:10.1016/j.apacoust.2006.09.003.

- Y. Pennec, B. Djafari Rouhani, H. Larabi, A. Akjouj, J.N. Gillet, J.O. Vasseur, G. Thabet, Phonon transport and waveguiding in a phononic crystal made up of cylindrical dots on a thin homogeneous plate. Physical Review B, 80(14) (2009) 144302. doi:10.1103/PhysRevB.80.144302.

- Y.M. Soliman, M.F. Su, Z.C. Leseman, C.M. Reinke, I. El-Kady, R.H. Olsson, III, Phononic crystals operating in the gigahertz range with extremely wide band gaps. Applied Physics Letters, 97(19) (2010). doi:10.1063/1.3504701.

- H. Xiang, Z. Shi, S. Wang, Y. Mo. Vibration attenuation and frequency band gaps in layered periodic foundation: theory and experiment. in Proceedings of the 15th World Conference on Earthquake Engineering. (2012), 3831-3839.

- H. Lv, X. Tian, M.Y. Wang, D. Li, Vibration energy harvesting using a phononic crystal with point defect states. Applied Physics Letters, 102(3) (2013). doi:10.1063/1.4788810.

- Y.-Y. Chen, Z. Ye, Propagation inhibition and wave localization in a two-dimensional random liquid medium. Physical Review E, 65(5) (2002) 056612. doi:10.1103/PhysRevE.65.056612.

- Y. Pennec. Propagation et localisation des ondes élastiques et électromagnétiques dans les matériaux phononiques, photoniques et plasmoniques. Université des Sciences et Technologies de Lille, 2010.

- Y. Pennec, B. Djafari-Rouhani, Fundamental properties of phononic crystal. Phononic crystals: Fundamentals and applications, (2016) 23-50.

- B. Gallas, Introduction aux métamatériaux, in Action Nationale Métrologie des indices pour les matériaux massifs, couches minces et liquides. Paris. (2009).

- Z. Liu, X. Zhang, Y. Mao, Y.Y. Zhu, Z. Yang, C.T. Chan, P. Sheng, Locally Resonant Sonic Materials. Science, 289(5485) (2000) 1734-1736. doi:10.1126/science.289.5485.1734.

- A. Amrane, N. Bourahla, A. Hassein-Bey, A. Khelif, Protection of structures subject to seismic and mechanical vibrations using periodical networks. Journal of Materials and Engineering Structures «JMES», 6(4) (2019) 565-581.

- A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, V. Laude, Complete band gaps in two-dimensional phononic crystal slabs. Physical Review E, 74(4) (2006) 046610. doi:10.1103/PhysRevE.74.046610.

- S. Brule, A. Bretschneider, I. Djeran-Maigre, L. Thorel. Métamatériaux sismiques et essais en centrifugeuses. in AFPS 2015 - 9ème Colloque National. CHAMPS-SUR-MARNE, France. (2015), 5p.

- J. Sánchez-Dehesa, A. Krokhin, Introduction to acoustics of phononic crystals. Homogenization at low frequencies, in Phononic Crystals: Fundamentals and Applications. Springer. (2016), 1-21. doi:10.1007/978-1-4614-9393-8_1.

- J.O. Vasseur, Des Matériaux Composites Pour De Nouveaux Isolants Phoniques, in Vers De Nouveaux Matériaux Et Dispositifs LDSMM, UFR de Physique, Université de Lille 1.

- A. Khelif, S. Mohammadi, A.A. Eftekhar, A. Adibi, B. Aoubiza, Acoustic confinement and waveguiding with a line-defect structure in phononic crystal slabs. Journal of Applied Physics, 108(8) (2010). doi:10.1063/1.3500226.


Refbacks

  • There are currently no refbacks.




Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

ISSN 2170-127X

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at http://revue.ummto.dz.