Vibration modes of mass‐loaded planoconvex quartz crystal resonators

1991 ◽  
Vol 90 (2) ◽  
pp. 700-706 ◽  
Author(s):  
Ewald Benes ◽  
Michael Schmid ◽  
Victor Kravchenko
Keyword(s):  
Quartz Crystal ◽  
Vibration Modes ◽  
Quartz Crystal Resonators

Electrical behaviour of AT-cut quartz crystal resonators as a function of overtone number

2010 ◽  
Vol 159 (2) ◽  
pp. 174-183 ◽  
Author(s):  
M. Cassiède ◽  
J.H. Paillol ◽  
J. Pauly ◽  
J.-L. Daridon
Keyword(s):  
Quartz Crystal ◽  
Electrical Behaviour ◽  
Quartz Crystal Resonators

scholarly journals Characterizing Vibrating Cantilevers for Liquid Viscosity and Density Sensing

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Christian Riesch ◽  
Erwin K. Reichel ◽  
Franz Keplinger ◽  
Bernhard Jakoby
Keyword(s):  
Cross Sections ◽  
Quartz Crystal ◽  
Model Parameters ◽  
Additional Mass ◽  
Liquid Loading ◽  
Fitting Procedure ◽  
Saw Devices ◽  
Quartz Crystal Resonators ◽  
Macroscopic Parameters ◽  
Online Process

Miniaturized liquid sensors are essential devices in online process or condition monitoring. In case of viscosity and density sensing, microacoustic sensors such as quartz crystal resonators or SAW devices have proved particularly useful. However, these devices basically measure a thin-film viscosity, which is often not comparable to the macroscopic parameters probed by conventional viscometers. Miniaturized cantilever-based devices are interesting alternatives for such applications, but here the interaction between the liquid and the oscillating beam is more involved. In our contribution, we describe a measurement setup, which allows the investigation of this interaction for different beam cross-sections. We present an analytical model based on an approximation of the immersed cantilever as an oscillating sphere comprising the effective mass and the intrinsic damping of the cantilever and additional mass and damping due to the liquid loading. The model parameters are obtained from measurements with well-known sample liquids by a curve fitting procedure. Finally, we present the measurement of viscosity and density of an unknown sample liquid, demonstrating the feasibility of the model.

scholarly journals Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates

Coatings ◽  
2020 ◽  
Vol 10 (7) ◽  
pp. 667
Author(s):  
Han Zhang ◽  
Yumei Chen ◽  
Ji Wang
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Quartz Crystal ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Superior Performance ◽  
Shear Modes ◽  
Practical Experiences ◽  
Quartz Crystal Resonators ◽  
Thickness Shear

A procedure based on approximate solutions of three-dimensional equations of wave propagation is utilized for calculating Bechmann’s number for the harmonic overtones of thickness-shear modes in the rotated Y-cut quartz crystal plates. Bechmann’s number is used for the optimization and improvement of electrodes to yield superior performance in the design of quartz crystal resonators. Originally, Bechmann’s number is found through practical experiences, and analytical results were provided afterward to enable optimal design of novel resonator structures. The outcomes in this study are from a simplified theoretical prediction and they are consistent with known empirical results, making it is possible to design optimal quartz crystal resonators for cases without adequate experimental data for a higher frequency and smaller size.

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