Free and forced vibrations of SC-cut quartz crystal rectangular plates with the first-order Mindlin plate equations.
Mindlin plate theory was used to provide accurate solutions to thickness-shear vibrations of plates, which have a much higher frequency than usual flexural vibrations and are the functioning modes of quartz crystal resonators. The vibration frequency solutions obtained with the Mindlin plate theory are proven being accurate along with mode shapes. In this paper, straight-crested wave solutions of free and forced vibrations of doubly rotated SC-cut of quartz crystal plates of rectangular shapes with four free edges are obtained with validated Mindlin plate equations. A procedure has been established for the calculation of dispersion relations, frequency spectra, mode shapes, and capacitance ratios of forced vibrations needed in resonator design.
Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China; Department of Architectural Engineering, Ningbo Polytechnic, 1069 Xinda Road, Beilun District, Ningbo, Zhejiang 315800, China.
Rongxing
R
Wu
Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China.
Wenjun
W
Wang
Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China.
Guijia
G
Chen
Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China.
Hui
H
Chen
Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China.
Tingfeng
T
Ma
Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China.
Jianke
J
Du
Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China. Electronic address: http://piezo.nbu.edu.cn/wangji.
Ji
J
Wang
Capacitance; Correction; Mindlin plate theory; Quartz crystal resonator; Thickness-shear vibration