Effects of asymmetric and nonuniform mass layers on quartz crystal microbalances

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.