title: Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals.
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.
authors.affiliation: College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, Zhejiang, China.
authors.forename: Jun
authors.initials: J
authors.lastname: Zhu
authors.affiliation: Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, Zhejiang, China.
authors.forename: Weiqiu
authors.initials: W
authors.lastname: Chen
authors.affiliation: Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0526, USA. Electronic address: jyang1@unl.edu.
authors.forename: Jiashi
authors.initials: J
authors.lastname: Yang
keywords: Phononic crystal; Plate; Wave