The thermal effect of metal electrodes on thickness-shear vibrations of crystal plates.
The effectiveness of theoretical approaches based on the initial thermal field on vibrations elastic solids has been demonstrated by a series of analyses concerning the thermal behavior of crystal resonators with results in good agreement with measurements. These equations have been implemented in a finite-element method in addition to simple analytical solutions we are familiar with. Starting with an infinite plate under a temperature increase in both crystal and metal layers, the frequency equation based on incremental thermal field formulation is obtained and solved analytically for thickness-shear vibrations with electrodes of different metals and configuration. Numerical examples show that the thermal effect of thicker electrodes on frequency-temperature relations of thickness-shear vibrations of AT-cut quartz crystal plates are generally positive and should be considered in the design process.
Piezoelectric Device Laboratory, School of Engineering, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China. wangji@nbu.edu.cn
Ji
J
Wang
Jianke
J
Du
Lijun
L
Shen
Zhihua
Z
Yang