Effects of the imperfect interface and viscoelastic loading on vibration characteristics of a quartz crystal microbalance

Abstract

The interfacial adhesion and viscoelasticity of an additional mass layer have a significant influence on the resonant frequency of a quartz crystal microbalance (QCM), especially when the attached mass layer is thick. In this study, a detailed quantitative investigation is conducted on the influence of the interface parameter and viscosity coefficient on the resonant frequency and admittance of a QCM. The obtained explicit expression of free vibration of the QCM can be numerically solved using Muller’s method. The results obtained in this study show that the viscoelasticity of the mass layer and its bonding characteristics significantly affect the performances of the QCM, such as the resonance frequency, displacement, and stress distributions, and the peak and bandwidth of admittance. The non-proportional relation between the resonance frequency and thickness of the mass layer becomes obvious when the thickness of the mass layer is larger than 2% that of the quartz plate. Meanwhile, the error between the exact solution and Sauerbrey’s solution is enlarged as the interface parameter increases or the viscosity coefficient decreases. The proposed method will be more precise in solving the resonant frequency than Sauerbrey’s equation does and able to provide a guidance for determining the viscosity of an attached mass layer. The novel points in the article are as follows: (i) The effects of the imperfect interface and viscosity on the resonance frequency of a QCM at different layer thicknesses are investigated. (ii) The difference between effects of the imperfect interface and viscosity on the characteristics of the admittance is discussed in detail.