Effects of Mass Layer Stiffness and Imperfect Bonding on a Quartz Crystal Microbalance

Abstract

We study free 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 its interface described by the so-called shear-slip model that allows a discontinuity of the interface displacement. The effect of mass layer in-plane shear stiffness is also considered. The equations of anisotropic elasticity are used for the crystal plate with the omission of the small elastic constant <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">56</sub> . The mass layer is governed by the plane-stress equations of elasticity. An analytical solution is obtained using Fourier series, from which the resonant frequencies and vibration mode shapes are calculated. The effects of the mass layer in-plane shear stiffness, imperfect interface bonding on resonant frequencies and energy trapping are examined.