Li Peng, Jin Feng, Sun Qing, Ma Jianxun
School of Human Settlements and Civil Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China.
Ultrasonics. 2015 Apr;58:96-103. doi: 10.1016/j.ultras.2014.12.007. Epub 2015 Jan 6.
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.
在石英晶体微天平（QCM）中，通常采用由附加质量层引起的惯性力来模拟有效的机械边界条件，而当上层相对较厚时，这可能会产生不正确的结果。因此，基于泰勒级数的二阶近似，对用于检测上层各向同性层特性的QCM中的厚度剪切振动进行了详细分析。用这种方法计算的结果比惯性力近似法具有更高的精度。根据这些结果，阐述了自由振动和受迫振动，以及在开启/关闭过程中或驱动电压幅度或频率突然波动时的瞬态效应。数值模拟表明，附加质量层对QCM的机械性能有很大影响，包括共振频率、位移和导纳幅度、瞬态过程的响应时间等。这些发现可为质量传感器装置中的物理现象解释和实验测量提供有效的指导。
