A Comparison of the Effects of Bending Moments on the Vibrations of AT and SC (or TTC) Cuts

Fletcher, E. D.; Douglas, Albert

doi:10.1109/freq.1979.200337

Cited by 13 publications

(8 citation statements)

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“…(1)- (6)) was demonstrated by comparing their 3-D finite element method model results with the experiment results by Mingins and Ballato [5] on an AT-cut circular disk of diameter d and thickness 2b, subjected to a pair of diametrical forces F at an angle ψ (azimuth angle) with the X1-axis as shown in Fig.2. The finite element software COMSOL 4.3b was employed for this study.…”

Section: Deformations Superposed On Finite Deformationsmentioning

confidence: 95%

“…The force sensitivity coefficient Kf as a function of the azimuth angle ψ were computed for the FEM model of Fletcher [6] plate and compared with the measured results of Ballato and Mingins [5]. These are shown in Figs.3 and 4 for the AT-cut and BT-cut, respectively.…”

Section: Deformations Superposed On Finite Deformationsmentioning

confidence: 99%

“…The incremental field variables and equations due to small amplitude of vibrations are shown in Table 1 and Eqns. (1) to (6). These equations are linear when the initial state is known, and are used to study the acceleration sensitivity of quartz crystal resonators and the effects of DC bias.…”

Section: Deformations Superposed On Finite Deformationsmentioning

confidence: 99%

“…The finite element software COMSOL 4.3b was employed for this study. The model plate dimensions were from Fletcher [6] with d=12 mm, gold electrodes of diameter 4 mm at center and ψ varying from 0° to 90°. The resonant mode used was the fundamental thickness shear mode.…”

Section: Deformations Superposed On Finite Deformationsmentioning

confidence: 99%

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Reduction of frequency deviations in quartz resonators by electric potentials of plate electrodes

Chen

Yong

Kubena

et al. 2014

2014 IEEE International Ultrasonics Symposium

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We present a new method in which a direct current (DC) bias field is used to control the resonant frequency of resonator subjected to body forces. The plate electrodes were used to create the DC bias field. Sensing electrodes were used to measure the body forces that cause the acceleration sensitivity. Finite element models were developed using the theory of small deformations superposed on finite initial deformations in Lagrangian formulation. The model results compared consistently well with the measured values for the force sensitivity coefficient Kf of a circular plate subjected to a pair of diametrical forces; hence validating our model for acceleration sensitivity. For our 1 GHz AT-cut quartz plate resonator with the crystal digonal X-axis perpendicular to plate X-axis, the inplane acceleration sensitivity is negligible, while the Y-axis acceleration sensitivity is maximum. A DC bias field with an appropriate DC bias voltage could yield a reduction in acceleration sensitivity from 10 -10 /g to 10 -12 /g in the Y-axis direction.

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Section: Deformations Superposed On Finite Deformationsmentioning

confidence: 95%

Section: Deformations Superposed On Finite Deformationsmentioning

confidence: 99%

Section: Deformations Superposed On Finite Deformationsmentioning

confidence: 99%

Section: Deformations Superposed On Finite Deformationsmentioning

confidence: 99%

See 2 more Smart Citations

Reduction of frequency deviations in quartz resonators by electric potentials of plate electrodes

Chen

Yong

Kubena

et al. 2014

2014 IEEE International Ultrasonics Symposium

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“…The resonator plate dimensions modeled are from Fletcher and Douglas's experimental setup [9] with d = 12 mm, centered silver electrodes of diameter 4 mm and ψ varying from 0° to 90°. The fundamental thickness shear mode is considered.…”

Section: Comparison Of Measured Data With 3-d Finite Element Modmentioning

confidence: 99%

On the acceleration sensitivity and its active reduction by edge electrodes in at-cut Quartz resonators

Chen

Yong

Kubena

et al. 2015

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Incremental piezoelectric equations for small vibrations superposed on initial deformations are presented. The equations are implemented in COMSOL finite element models (FEA). Equations are validated by comparing the results for the force sensitivity coefficient Kf of a circular quartz plate subjected to a pair of diametrical forces with measured data. The model results show a consistent trend with the experimental results, and the relative difference between our FEA results and Ballato's measured result is about 13%. A detailed study of the acceleration sensitivity of a rectangular AT-cut quartz plate is presented. The plate resonator is fixed along one edge as a cantilever. For AT-cut quartz resonators with the crystal digonal X-axis perpendicular to plate X-axis, the in-plane acceleration sensitivity is found to be negligible compared with the out-of-plane (Y-axis) acceleration sensitivity. For AT-cut quartz resonators with the crystal digonal X-axis parallel to plate X-axis, the Y-axis acceleration sensitivity is found to be rectified, that is the fractional change in frequency is positive with respect to both positive and negative Y-axis accelerations. The Y-axis acceleration sensitivity is small in comparison with the in-plane acceleration sensitivity for small body forces. However, for large body forces, the Y-axis acceleration sensitivity dominates because it increases nonlinearly with the Y-axis acceleration. The resonator rectified acceleration sensitivity is confirmed by phase noise measurements. For reduced acceleration sensitivity, two pairs of electrodes along the plate edges reduce the bending of the plate resonator and subsequently reduce acceleration sensitivity. We present a new method using these edge electrodes in which a dc bias field is employed to control the resonant frequency of resonator subjected to g body forces. A dc bias field with an appropriate dc bias voltage could potentially yield a reduction of acceleration sensitivity in Y-axis direction of about two orders of magnitude.

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Experimental studies in magnetically induced transverse force-frequency effect in thin quartz microresonators

Hatipoglu

Tadigadapa

2015

Journal of Applied Physics

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In this work, the transverse force-frequency sensitivity of magnetostrictive Metglas® (Fe85B5Si10) thin film coated AT-cut thickness shear mode quartz thin plate microresonator (500 μm × 500 μm × 19 μm) is experimentally measured and modeled in Lagrangian formulation by coupling magnetostrictive deformation equations with the basic plate equations from the theory of small deformation. The quartz plate resonator is fabricated by micromachining techniques and released into fixed-free structure using focused ion beam milling. Application of a magnetic field results in the out-of-plane bending of the structure due to elastic coupling between the magnetostrictive Metglas® and quartz resonator layers. As a result of the transverse loading and out-of-plane bending, the admittance characteristics of the resonator shifts, and these shifts are recorded in real time utilizing a network analyzer. The sensitivity is experimentally measured to be 162.3 mdeg/Oe for phase, corresponding to a frequency sensitivity of Δf/H = 11 Hz/Oe. The equivalent force-frequency sensitivity can then be calculated as 2.36 μN/Hz using the developed model. The coupled domain analysis fits well with the experimental data. Further reduction of quartz thickness and optimization of the thickness ratio of the magnetostrictive to quartz layers offers the possibility of exploiting the stress sensitivity of plate microresonators as sensitive magnetic field sensors capable of low nanoTesla to picoTesla level magnetic flux densities.

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A Comparison of the Effects of Bending Moments on the Vibrations of AT and SC (or TTC) Cuts

Cited by 13 publications

References 0 publications

Reduction of frequency deviations in quartz resonators by electric potentials of plate electrodes

Reduction of frequency deviations in quartz resonators by electric potentials of plate electrodes

On the acceleration sensitivity and its active reduction by edge electrodes in at-cut Quartz resonators

Experimental studies in magnetically induced transverse force-frequency effect in thin quartz microresonators

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