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.
Wang
Ji
J
Piezoelectric Device Laboratory, School of Engineering, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China. wangji@nbu.edu.cn
Du
Jianke
J
Shen
Lijun
L
Yang
Zhihua
Z