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Elastic Wave Propagation in Anisotropic and Functionally Graded Layered Phononic Crystals: Band-Gaps, Pass-Bands and Low Transmission Pass-Bands

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Advanced Materials

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Abstract

This paper describes a mathematical model of plane wave propagation in anisotropic and functionally graded layered phononic crystals with finite and infinite number of unit-cells. Classification of pass-bands and band-gaps is presented based on asymptotic analysis of the wave-fields in periodic layered structures. Two kinds of band-gaps where the transmission coefficient decays exponentially with the number of unit-cells are specified. The so-called low transmission pass-bands are introduced in order to identify frequency ranges in which the transmission is low enough for engineering applications, but it does not tend to zero exponentially with the number of unit-cells approaching infinity. The results of the numerical simulation are presented in order to demonstrate wave propagation phenomena. The influence of the anisotropy and functionally graded interlayers on the band-gaps and pass-bands is analysed.

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Acknowledgements

The work is supported by the Russian Foundation for Basic Research grants 16-41-230352, 16-51-53043 (joint RFBR-NSFC project 11611130017), the grant of the President of the Russian Federation (MK-7154.2015.1) and Ministry of Science and Education of Russian Federation (Project 1.189.2014K).

Author information

Authors and Affiliations

  1. Institute for Mathematics, Mechanics and Informatics, Kuban State University, Stavropolskaya Str., 149, Krasnodar, 350040, Russia

    Mikhail V. Golub, Sergey I. Fomenko & Andrey A. Alexandrov

  2. Chair of Structural Mechanics, Department of Civil Engineering, University of Siegen, Paul-Bonatz Strasse 9-11, 57076, Siegen, Germany

    Chuanzeng Zhang

  3. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing, 100044, PR China

    Yue-Sheng Wang & A-Li Chen

Authors
  1. Mikhail V. Golub
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  2. Sergey I. Fomenko
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  3. Andrey A. Alexandrov
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  4. Chuanzeng Zhang
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  5. Yue-Sheng Wang
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  6. A-Li Chen
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Corresponding author

Correspondence to Mikhail V. Golub .

Editor information

Editors and Affiliations

  1. Mathematics, Mechanics and Computer Sciences Institute, Southern Federal University Math., Mech. and CS Inst., Rostov-on-Don, Russia

    Ivan A. Parinov

  2. Department of Microelectronics Engineering, National Kaohsiung Marine University Dept. of Microelectronics Eng., Kaohsiung, Taiwan

    Shun-Hsyung Chang

  3. Fakultas Teknik, University of 17 Agustus 1945 Surabaya , Surabaya, Indonesia

    Muaffaq A. Jani

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© 2017 Springer International Publishing AG

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Cite this paper

Golub, M.V., Fomenko, S.I., Alexandrov, A.A., Zhang, C., Wang, YS., Chen, AL. (2017). Elastic Wave Propagation in Anisotropic and Functionally Graded Layered Phononic Crystals: Band-Gaps, Pass-Bands and Low Transmission Pass-Bands. In: Parinov, I., Chang, SH., Jani, M. (eds) Advanced Materials. Springer Proceedings in Physics, vol 193. Springer, Cham. https://doi.org/10.1007/978-3-319-56062-5_23

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