title: The properties of thickness-twist (TT) wave modes in a rotated Y-cut quartz plate with a functionally graded material top layer.
abstract: We propose the use of thickness-twist (TT) wave modes of an AT-cut quartz crystal plate resonator for measurement of material parameters, such as stiffness, density and material gradient, of a functionally graded material (FGM) layer on its surface, whose material property varies exponentially in thickness direction. A theoretical analysis of dispersion relations for TT waves is presented using Mindlin's plate theory, with displacement mode shapes plotted, and the existence of face-shear (FS) wave modes discussed. Through numerical examples, the effects of material parameters (stiffness, density and material gradient) on dispersion curves, cutoff frequencies and mode shapes are thoroughly examined, which can act as a theoretical reference for measurements of unknown properties of FGM layer.
authors.affiliation: State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, 29 Yudao Jie, Nanjing 210016, China.
authors.forename: Bin
authors.initials: B
authors.lastname: Wang
authors.affiliation: State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, 29 Yudao Jie, Nanjing 210016, China. Electronic address: qianzh@nuaa.edu.cn.
authors.forename: Zhenghua
authors.initials: Z
authors.lastname: Qian
authors.affiliation: State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, 29 Yudao Jie, Nanjing 210016, China.
authors.forename: Nian
authors.initials: N
authors.lastname: Li
authors.affiliation: State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, 29 Yudao Jie, Nanjing 210016, China; Western Governors University Washington, 1001 Fourth Avenue, Seattle, WA 98154-1101, USA.
authors.forename: Hamid
authors.initials: H
authors.lastname: Sarraf
mesh_terms: D004548:Elasticity; D008420:Manufactured Materials; D011791:Quartz; D012399:Rotation; D013314:Stress, Mechanical; D013499:Surface Properties; D014465:Ultrasonics
chemical_list: D011791:Quartz
keywords: Dispersion curves; Functionally graded materials; Quartz; Thickness-twist waves