title: Thickness-shear and thickness-twist modes in an AT-cut quartz acoustic wave filter.
abstract: We studied thickness-shear and thickness-twist vibrations of a monolithic, two-pole crystal filter made from a plate of AT-cut quartz. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded quartz plates were employed which are valid for both the fundamental and the overtone modes. Exact solutions for the free vibration resonant frequencies and modes were obtained from the equations. For a structurally symmetric filter, the modes can be separated into symmetric and antisymmetric ones. Trapped modes with vibrations mainly under the electrodes were found. The effect of the distance between the two pairs of electrodes was examined.
authors: State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
authors: Zinan
authors: Z
authors: Zhao
authors: State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. Electronic address: qianzh@nuaa.edu.cn.
authors: Zhenghua
authors: Z
authors: Qian
authors: State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
authors: Bin
authors: B
authors: Wang
authors: Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0526, USA.
authors: Jiashi
authors: J
authors: Yang
keywords: Energy trapping; Filter; Plate; Thickness-shear; Thickness-twist