Effects of Mass Layer Nonuniformity 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 (TSh) vibration of an AT-cut quartz plate with a nonuniform mass layer. Mindlin's 2-D equation for TSh vibration of a quartz plate is used. An elliptical mass layer with stepped thickness is considered which allows an exact analysis based on the plate equation. Free vibration frequencies and modes are obtained. The effects of the mass layer nonuniformity are examined. Results show that a mass layer thicker at the center tends to confine more modes under the mass layer and push the distribution of the TSh displacement toward the center.