Effects of a Mass Layer With Gradually Varying Thickness on a Quartz Crystal Microbalance

We study the effects of the nonuniform thickness of a thin mass layer on a quartz crystal microbalance. A theoretical analysis is performed on thickness-shear vibration of an AT-cut quartz plate with a nonuniform mass layer. Mindlin´s two-dimensional equation for thickness-shear vibration of a quartz plate is used. Free vibration frequencies and modes are obtained. The effects of the mass layer nonuniformity are examined. It is shown that resonant frequencies and energy trapping of thickness-shear modes are sensitive to mass layer nonuniformity.