A Theoretical Model for Analyzing the Thickness-Shear Vibration of a Circular Quartz Crystal Plate With Multiple Concentric Ring Electrodes

Uniform Mass Sensitivity Distribution of Elliptically Designed Electrodes Based on a Quartz Crystal Microbalance

“…The existing investigation methods concerning the QCM mainly include experiments, , the three-dimensional (3D) finite element method (FEM), − and two-dimensional (2D) theoretical analysis. − Before an experiment, a numerical or theoretical investigation on the basic characteristics and parameter optimization of the QCM is helpful to the experimental design. Numerical techniques and 3D FEM, in particular, are gradually replacing the analytical treatments. − Compared to 2D theoretical analysis, 3D FEM is more flexible with regard to geometry.…”

“…There is a phenomenon in the 3D model of the ring- and double-ring-type QCM: the amplitude of vibration on the surface of the QCM sensor perpendicular to the direction of displacement is enhanced in the vibration distribution of the QCM. This phenomenon exists in the vibration distribution of circular and rectangular single-ring electrodes, ,, as well as circular double-ring electrodes and even multiple concentric ring electrodes. , However, there is no simple physical reason for why this phenomenon occurs. We have conducted the corresponding research and hypothesized that the phenomenon may be due to the strengthening of the trapping effect.…”

“…This phenomenon exists in the vibration distribution of circular and rectangular single-ring electrodes, 14,22,23 as well as circular double-ring electrodes and even multiple concentric ring electrodes. 16,24 However, there is no simple physical reason for why this phenomenon occurs. We have conducted the corresponding research and hypothesized that the phenomenon may be due to the strengthening of the trapping effect.…”

An analytical and meshless modeling for vibration analysis of an infinite quartz resonator with non-circular electrodes

“…After coordinate transformation, the displacement component in different regions is expressed in the form of Bessel functions, and the Fourier series expansion is adopted for satisfying the continuous boundary in Section 2. Different from the perturbation method developed by Tiersten [23] and the collocation method conducted by Wang et al [7] and Zhu et al [26], the theoretical solutions proposed in this paper is more rigorous with more accuracy, which can strictly satisfy the dynamic governing equations and the corresponding boundary conditions. In Section 3, the convergence of this series is illustrated, and the theoretical solution is validated by comparing the resonant frequencies and mode shapes with those from the COMSOL Multiphysics software.…”

“…Most of electrodes in QCRs are rectangular. In recent years, circular [7], polygonal [8], elliptical [9,10] or other electrodes with different profiles [11] are introduced into the resonators, which also exhibit good performances at trapping vibration energy. Not limited by this, the electrodes with complex profile can efficiently suppress spurious modes unwanted.…”