Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum

Sourav Banerjee; Riaz Uddin Ahmed

doi:doi:10.11648/j.ijmsa.20140301.12

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Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum

Sourav Banerjee, Riaz Uddin Ahmed

Published in International Journal of Materials Science and Applications (Volume 3, Issue 1)

Received: 7 December 2013 Published: 10 January 2014

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Abstract

Periodic and chiral orientation of microstructures, here we call phononic crystals, have extraordinary capabilities to facilitate the innovative design of new generation metamaterials. Periodic arrangements of phononic crystals are capable of opening portals of non-passing, non-dispersive mechanical waves. Defying conventional design of regular periodicity, in this paper spirally periodic but chiral orientation of resonators are envisioned. Dynamics of the spirally connected resonators and the acoustic wave propagation through the spirally connected multiple local resonators are studied using fundamental physics. In present study the spiral systems with local resonators are assumed to be discrete media immersed in fluid. In this paper it is assumed that acoustic or ultrasonic waves in fluid are propagated along the plane of the spiral resonators and thus only the longitudinal wave mode exists due to nonexistence of shear stress in the fluid. Lagrangian formulation of the spiral systems were employed to obtain the governing Euler-Lagrange equation of the system. Discrete element method was employed to verify the equation assuming nearest neighboring effect.

Published in	International Journal of Materials Science and Applications (Volume 3, Issue 1)
DOI	10.11648/j.ijmsa.20140301.12
Page(s)	6-13
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Spiral Resonators, Phonon Confinement, Discrete Continuum Model, Spiral Metamaterials

References

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[2]	Li, X., Liu, Z.Y., (2005). Coupling of cavity modes and guiding modes in two-dimensional phononic crystals. Solid State Commun. 133, 397.
[3]	Poulton, C. G., Movchan, A. B., McPhedran, R. C., Nicorovici, N. A., and Antipov, Y. A., (2000). Eigenvalue Problems for Doubly Periodic Elastic Structures and Phononic Band Gaps. Proc. R. Soc. London, Ser. A, 456, 2543–2559.
[4]	Xu, Y. L., Chen, C. Q., Tian, X. G., (2013). Phonon-polarization and band structure of electro-magneto-acoustic SH wave propagation oblique to the periodic layers piezoelectric. Physics Letters A., 377, 895-902.
[5]	Li, J., and Chan, C. T., (2004). Double-Negative Acoustic Metamaterial. Phys. Rev. E, 70, 055602.
[6]	Yao, S. S., Zhou, X. M., and Hu, G. K., (2008). Experimental Study on Negative Effective Mass in a 1D Mass-Spring System. New J. Phys., 10, 043020
[7]	Hirsekorn, M., Delsanto, P.P., Batra, N. K., Matic, P., (2004). Modelling and simulation of acoustic wave propagation in locally resonant sonic materials. Ultrasonics, 42(19), 231-235.
[8]	Hsu, J. C., (2011). Local resonances-induced low-frequency band gaps in two-dimensional phononic crystal slabs with periodic stepped resonators. J. Phys. D: Appl. Phys., 44, 055401.
[9]	Caballero, D., S'anchez-Dehesa, J., Rubio, C., M'artinez-Sala, R., S'anchez-P'erez, J., V., Meseguer, F., Llinares, J., (1999). Large two-dimensional sonic band gaps. Phys. Rev. E, 60(6), R6316-R6319.
[10]	Caballero, D., S'anchez-Dehesa, J., Rubio, C., M'artinez-Sala, R., S'anchez-P'erez, J., V., Meseguer, F., Llinares, J., (1999). Large two-dimensional sonic band gaps. Phys. Rev. E, 60(6), R6316-R6319.
[11]	Liu, Z., Chan, C. T., and Sheng, P., (2005). Analytic Model of Phononic Crystals WithLocal Resonances. Phys. Rev. B, 71, 014103.
[12]	Mainzer, K., Symmetries of Nature: A Handbook for Philosophy of Nature and Science, Walter de Gruyter& Co., ISBN 3-11-012990-6, 1998.
[13]	Nemer, S., Sauviac, B., Bayard, B., Nader, C., Bechara, J., and Khoury, A., (2011). Modelling resonance frequencies of a multi-turn spiral for metamaterial applications. Progress In Electromagnetics Research C, 20, 31-42.
[14]	Baena, J., Marqués, R., Medina, F., & Martel, J., (2004). Artificial magnetic metamaterial design by using spiral resonators. Physical Review B, 69(1), 1-5.
[15]	He, M., Han, J., Tian, Z., Gu, J., Xing, Q., (2011). Negative refractive index in chiral spiral metamaterials at terahertz frequencies. Optik - International Journal for Light and Electron Optics, 122(18), 1676-1679.
[16]	Isik, O., Esselle, K., P., (2009). Analysis of spiral metamaterials by use of group theory. Metamaterials, 3(1), 33-43.
[17]	Elford, D., P., Chalmers, L., Kusmartsev, F., V., Shallowe, G., M., (2010). Acoustic band gap formation in metamaterials. International Journal of Modern Physics B, 24 (25-26), 4935-4945.
[18]	Goldstein, H., Poole, P. Charles, Safko, J., Classical Mechanics, Pearson, ISBN 978-81-317-5891-5, 2011.

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Sourav Banerjee, Riaz Uddin Ahmed. (2014). Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum. International Journal of Materials Science and Applications, 3(1), 6-13. https://doi.org/10.11648/j.ijmsa.20140301.12

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ACS Style

Sourav Banerjee; Riaz Uddin Ahmed. Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum. Int. J. Mater. Sci. Appl. 2014, 3(1), 6-13. doi: 10.11648/j.ijmsa.20140301.12

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AMA Style

Sourav Banerjee, Riaz Uddin Ahmed. Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum. Int J Mater Sci Appl. 2014;3(1):6-13. doi: 10.11648/j.ijmsa.20140301.12

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@article{10.11648/j.ijmsa.20140301.12,
  author = {Sourav Banerjee and Riaz Uddin Ahmed},
  title = {Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum},
  journal = {International Journal of Materials Science and Applications},
  volume = {3},
  number = {1},
  pages = {6-13},
  doi = {10.11648/j.ijmsa.20140301.12},
  url = {https://doi.org/10.11648/j.ijmsa.20140301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmsa.20140301.12},
  abstract = {Periodic and chiral orientation of microstructures, here we call phononic crystals, have extraordinary capabilities to facilitate the innovative design of new generation metamaterials. Periodic arrangements of phononic crystals are capable of opening portals of non-passing, non-dispersive mechanical waves. Defying conventional design of regular periodicity, in this paper spirally periodic but chiral orientation of resonators are envisioned. Dynamics of the spirally connected resonators and the acoustic wave propagation through the spirally connected multiple local resonators are studied using fundamental physics. In present study the spiral systems with local resonators are assumed to be discrete media immersed in fluid. In this paper it is assumed that acoustic or ultrasonic waves in fluid are propagated along the plane of the spiral resonators and thus only the longitudinal wave mode exists due to nonexistence of shear stress in the fluid. Lagrangian formulation of the spiral systems were employed to obtain the governing Euler-Lagrange equation of the system. Discrete element method was employed to verify the equation assuming nearest neighboring effect.},
 year = {2014}
}

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TY  - JOUR
T1  - Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum
AU  - Sourav Banerjee
AU  - Riaz Uddin Ahmed
Y1  - 2014/01/10
PY  - 2014
N1  - https://doi.org/10.11648/j.ijmsa.20140301.12
DO  - 10.11648/j.ijmsa.20140301.12
T2  - International Journal of Materials Science and Applications
JF  - International Journal of Materials Science and Applications
JO  - International Journal of Materials Science and Applications
SP  - 6
EP  - 13
PB  - Science Publishing Group
SN  - 2327-2643
UR  - https://doi.org/10.11648/j.ijmsa.20140301.12
AB  - Periodic and chiral orientation of microstructures, here we call phononic crystals, have extraordinary capabilities to facilitate the innovative design of new generation metamaterials. Periodic arrangements of phononic crystals are capable of opening portals of non-passing, non-dispersive mechanical waves. Defying conventional design of regular periodicity, in this paper spirally periodic but chiral orientation of resonators are envisioned. Dynamics of the spirally connected resonators and the acoustic wave propagation through the spirally connected multiple local resonators are studied using fundamental physics. In present study the spiral systems with local resonators are assumed to be discrete media immersed in fluid. In this paper it is assumed that acoustic or ultrasonic waves in fluid are propagated along the plane of the spiral resonators and thus only the longitudinal wave mode exists due to nonexistence of shear stress in the fluid. Lagrangian formulation of the spiral systems were employed to obtain the governing Euler-Lagrange equation of the system. Discrete element method was employed to verify the equation assuming nearest neighboring effect.
VL  - 3
IS  - 1
ER  -

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Author Information

Sourav Banerjee

Dept. of Mechanical Engineering, University of South Carolina, Columbia, South Carolina, USA
Riaz Uddin Ahmed

Dept. of Mechanical Engineering, University of South Carolina, Columbia, South Carolina, USA

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APA Style

Sourav Banerjee, Riaz Uddin Ahmed. (2014). Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum. International Journal of Materials Science and Applications, 3(1), 6-13. https://doi.org/10.11648/j.ijmsa.20140301.12

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ACS Style

Sourav Banerjee; Riaz Uddin Ahmed. Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum. Int. J. Mater. Sci. Appl. 2014, 3(1), 6-13. doi: 10.11648/j.ijmsa.20140301.12

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AMA Style

Sourav Banerjee, Riaz Uddin Ahmed. Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum. Int J Mater Sci Appl. 2014;3(1):6-13. doi: 10.11648/j.ijmsa.20140301.12

Copy | Download

@article{10.11648/j.ijmsa.20140301.12,
  author = {Sourav Banerjee and Riaz Uddin Ahmed},
  title = {Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum},
  journal = {International Journal of Materials Science and Applications},
  volume = {3},
  number = {1},
  pages = {6-13},
  doi = {10.11648/j.ijmsa.20140301.12},
  url = {https://doi.org/10.11648/j.ijmsa.20140301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmsa.20140301.12},
  abstract = {Periodic and chiral orientation of microstructures, here we call phononic crystals, have extraordinary capabilities to facilitate the innovative design of new generation metamaterials. Periodic arrangements of phononic crystals are capable of opening portals of non-passing, non-dispersive mechanical waves. Defying conventional design of regular periodicity, in this paper spirally periodic but chiral orientation of resonators are envisioned. Dynamics of the spirally connected resonators and the acoustic wave propagation through the spirally connected multiple local resonators are studied using fundamental physics. In present study the spiral systems with local resonators are assumed to be discrete media immersed in fluid. In this paper it is assumed that acoustic or ultrasonic waves in fluid are propagated along the plane of the spiral resonators and thus only the longitudinal wave mode exists due to nonexistence of shear stress in the fluid. Lagrangian formulation of the spiral systems were employed to obtain the governing Euler-Lagrange equation of the system. Discrete element method was employed to verify the equation assuming nearest neighboring effect.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Phonon Confinement Using Spirally Designed Elastic Resonators in Discrete Continuum
AU  - Sourav Banerjee
AU  - Riaz Uddin Ahmed
Y1  - 2014/01/10
PY  - 2014
N1  - https://doi.org/10.11648/j.ijmsa.20140301.12
DO  - 10.11648/j.ijmsa.20140301.12
T2  - International Journal of Materials Science and Applications
JF  - International Journal of Materials Science and Applications
JO  - International Journal of Materials Science and Applications
SP  - 6
EP  - 13
PB  - Science Publishing Group
SN  - 2327-2643
UR  - https://doi.org/10.11648/j.ijmsa.20140301.12
AB  - Periodic and chiral orientation of microstructures, here we call phononic crystals, have extraordinary capabilities to facilitate the innovative design of new generation metamaterials. Periodic arrangements of phononic crystals are capable of opening portals of non-passing, non-dispersive mechanical waves. Defying conventional design of regular periodicity, in this paper spirally periodic but chiral orientation of resonators are envisioned. Dynamics of the spirally connected resonators and the acoustic wave propagation through the spirally connected multiple local resonators are studied using fundamental physics. In present study the spiral systems with local resonators are assumed to be discrete media immersed in fluid. In this paper it is assumed that acoustic or ultrasonic waves in fluid are propagated along the plane of the spiral resonators and thus only the longitudinal wave mode exists due to nonexistence of shear stress in the fluid. Lagrangian formulation of the spiral systems were employed to obtain the governing Euler-Lagrange equation of the system. Discrete element method was employed to verify the equation assuming nearest neighboring effect.
VL  - 3
IS  - 1
ER  -

Copy | Download