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Zhu J, Chen W, Yang J. Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals. Ultrasonics. 2014;54(7):1899-903doi: 10.1016/j.ultras.2014.05.016.
Zhu, J., Chen, W., & Yang, J. (2014). Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals. Ultrasonics, 54(7), 1899-903. https://doi.org/10.1016/j.ultras.2014.05.016
Zhu, Jun, et al. "Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals." Ultrasonics vol. 54,7 (2014): 1899-903. doi: https://doi.org/10.1016/j.ultras.2014.05.016
Zhu J, Chen W, Yang J. Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals. Ultrasonics. 2014 Sep;54(7):1899-903. doi: 10.1016/j.ultras.2014.05.016. Epub 2014 Jun 02. PMID: 24924785.
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Ultrasonics. 2014 Sep;54(7):1899-903. doi: 10.1016/j.ultras.2014.05.016. Epub 2014 Jun 02.

Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals.

Ultrasonics

Jun Zhu, Weiqiu Chen, Jiashi Yang

Affiliations

  1. College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, Zhejiang, China.
  2. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, Zhejiang, China.
  3. Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0526, USA. Electronic address: [email protected].

PMID: 24924785 DOI: 10.1016/j.ultras.2014.05.016

Abstract

We study the propagation of thickness-twist (TT) waves in a crystal plate of AT-cut quartz with periodically varying, piecewise constant thickness. The scalar differential equation by Tiersten and Smythe is employed. The problem is found to be mathematically equivalent to the motion of an electron in a periodic potential field governed by Schrodinger's equation. An analytical solution is obtained. Numerical results show that the eigenvalue (frequency) spectrum of the waves has a band structure with allowed and forbidden bands. Therefore, for TT waves, plates with periodically varying thickness can be considered as phononic crystals. The effects of various parameters on the frequency spectrum are examined.

Copyright © 2014 Elsevier B.V. All rights reserved.

Keywords: Phononic crystal; Plate; Wave

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