The application of second-order approximation of Taylor series in thickness shear vibration analysis of quartz crystal microbalances

The inertia force caused by an additional mass layer is usually adopted to simulate the effective mechanical boundary condition in a quartz crystal microbalance (QCM), which may yield incorrect results when the upper layer becomes relative thicker. Thus, a detail analysis of the thickness shear vibration in a QCM for detecting the characteristics of the upper isotropic layer is proceeded based on a second-order approximation of Taylor series. The result calculated by this method has a higher accuracy than that of inertial-force approximation. According to these outcomes, the free and forced vibration has been illustrated, as well as transient effects during the switching on/off processes or under a sudden fluctuation of the driving-voltage amplitude or frequency. It has been revealed by numerical simulation that the additional mass layer has a great influence on the mechanical performance of QCM, including the resonance frequency, amplitudes of displacement and admittance, response time of the transient processes, and so on. These findings can prove effective guidance for physical phenomenon explanations and experimental measurement in mass sensor devices.