Acta Mechanica

, Volume 230, Issue 6, pp 2187–2200 | Cite as

Dispersion feature of elastic waves in a 1-D phononic crystal with consideration of couple stress effects

  • Yueqiu LiEmail author
  • Peijun Wei
  • Changda Wang
Original Paper


The couple stress effects upon the propagation behavior and the dispersive feature of Bloch waves in the periodically laminated structure are studied in this paper. First, the various modes of wave motion in the elastic solid with consideration of the couple stress are formulated. Apart from the dispersive P wave, SV wave, and SH wave, there are two evanescent waves, namely SS wave and SSH wave. These modes of wave motion are considered to formulate the state vector and further the transfer matrix in each layer. Then, the non-classic interface continuity conditions with consideration of couple stress effects are used to derive the transfer matrix of the state vector in a typical single cell. At last, the Bloch theorem is used to give the dispersive equations of Bloch waves in the periodical structure. The in-plane Bloch waves and the anti-plane Bloch waves which propagate either obliquely or vertically are both considered in the present work. The numerical results are obtained by solving the dispersive equations and shown graphically. The influences of the couple stress effects on the propagation and the dispersive feature of Bloch waves are discussed based on the numerical results.


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The work is supported by Fundamental Research Funds for the Central Universities (FRF-BR-15-026A), National Natural Science Foundation of China (No. 11872105), National Natural Science Foundation of China (No. 51701099), State science and technology support program (No. 2013BAK12B08) and HeiLongJiang Natural Science Fund (No. B2015019), and The Fundamental Research Funds in HeiLongJiang Provincial Universities (No. 135109232).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsQiqihar UniversityQiqiharChina
  2. 2.Department of Applied MechanicsUniversity of Science and Technology BeijingBeijingChina
  3. 3.State Key Laboratory of High-Efficient Mining and Safety of Metal MinesUniversity of Science and Technology BeijingBeijingChina

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