Effects of mass layer imperfect bonding on the electrical impedance of a quartz crystal microbalance

We study electrically forced vibrations of a crystal plate of AT-cut quartz carrying a thin mass layer operating as a quartz crystal microbalance for mass sensing. The mass layer is imperfectly bonded to the crystal plate with their interface described by the so-called interface-slip model which allows a discontinuity of the tangential interface displacement. Mindlin's equations for piezoelectric plates are used. An analytical solution is obtained. The electrical impedance is calculated. The effects of an elastic interface and a viscoelastic interface are examined.