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Updated: Apr 28, 2026

Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing
Published on: June 28, 2024
Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals
Jun Zhu1, Weiqiu Chen2, Jiashi Yang3
1College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, Zhejiang, China.
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.
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