Effects of asymmetric and nonuniform mass layers on quartz crystal microbalances

Abstract

The free vibrations of an AT-cut quartz plate carrying a thin mass layer operating as a quartz crystal microbalance for mass sensing is presented. More general than previous studies, the mass layer may be nonuniform and asymmetric. The equations of anisotropic elasticity are used to model the quartz crystal plate with the omission of the small elastic constant c ₅₆. An analytical solution is obtained using Fourier series from which the resonant frequencies and the vibration mode shapes are calculated. The effects of mass layer nonuniformity and asymmetry on the resonant frequencies and mode shapes as well as the vibration confinement by the mass layer are examined.

Keywords:

• elastic waves
• sensors
• mechanics

Acknowledgments

This study was supported by the Phase III Construction of the “985” Project of Sun Yat-sen University. The authors acknowledge the support of the Introduction of Innovative R&D Team Project of Guangdong Province. They also acknowledge the support of the Science and Technology Planning Project of Guangdong Province (no. 2011A060901013) and the Science and Technology Planning Project of Guangzhou (no. 2011Y1-00029). This study was also supported by the Industry-Universities-Research Cooperation Project of Guangdong Province and Ministry of Education of China (no. 2011A090200123). Partial support by the US Army Research laboratory/US Army Research Office under agreement number W911NF-10-1-0293 is also acknowledged.