Reactions of a Vibrating Piezoelectric Crystal Plate to Externally Applied Forces

Mingins, C.R.; Barcus, L.C.; Perry, Robert W.

doi:10.1109/freq.1963.201254

Cited by 11 publications

(2 citation statements)

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“…6. The present and Lee et al's [22] analytical results follow sine functions, whereas the experimental results presented in literature [29], [29], [30] show that the frequency changes are a combination of two sine functions. This could be caused by the use of the stresses at the center of the QXR as the calculation reference to simplify the more complex stress distributions in analysis.…”

Section: Frequency Changescontrasting

confidence: 42%

Effect of transverse force on the performance of quartz resonator force sensors

Wang

Dong

Zhu

et al. 2004

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

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This paper discusses the effect of transverse force on the performance of quartz crystal resonator (QXR) force sensors that use symmetrical incomplete circular QXRs as sensing elements. Based on Lee's vibration theory and the transverse force-induced stress distribution, frequency changes are derived. This result and finite element method (FEM) are applied to investigate the performance of two metal-quartz combined sensors under the action of transverse force. Analytical and experimental results show that transverse force affects the sensitivity and linearity of QXR force sensors.

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Section: Frequency Changescontrasting

confidence: 42%

Effect of transverse force on the performance of quartz resonator force sensors

Wang

Dong

Zhu

et al. 2004

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

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“…Finite strain takes the form of the Green strain tensor or Lagrangian (1) in which u7 is the small-field dynamic displacement vector. Components of u y in the notation of References 36, 39 and 42 are given by (4) where SKL is the Cauchy infinitesimal strain tensor. Following the convention used in References 36, 39 and 42, capital and lowercase indices refer to the Cartesian components for the original undisturbed and the present co-ordinates of material points, respectively.…”

Section: Perturbation Integralmentioning

confidence: 99%

Quartz resonator frequency shifts computed using the finite element method

Clayton¹,

EerNisse²

1993

Numerical Meth Engineering

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SUMMARYA new solution technique has been developed to calculate the frequency shifts arising from mechanical stresses in the case of quartz resonators. This solution technique utilizes finite element analysis as an initial step to calculate mechanical stress distributions in quartz resonators. Output from the finite element solution is used in a recently developed program to calculate resonator frequency shifts as the final step. Frequency shifts are calculated via numerical integration of the perturbation integral derived by T i e r~t e n .~~ The solution technique is general in that any combination of mount and resonator geometries may be modelled. Any crystallographic orientation may be chosen and any load or combination of loads may be applied to the resonator. The frequency perturbation calculation includes movement of the mode to any position in the general vicinity of the resonator centre. Experimental results for AT-and SC-cut quartz resonators subjected to diametric forces and inertial loading verify the accuracy of frequency shifts calculated using the new solution technique.

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The acceleration sensitivity of quartz crystal oscillators: a review

Filler

1988

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

169

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A tutorial on navigation, radar, and identification systems is presented. The topics discussed are the consequences of acceleration sensitivity in crystal oscillators on the Allan variance, including the effects of sinusoidal and random vibration, phase noise and integrated phase jitter; the vector nature of quartz resonator sensitivity; the theoretical description of the cause of the acceleration sensitivity of quartz resonators; techniques for the measurement of acceleration sensitivity; and the effect of frequency multiplication on acceleration effect. Various techniques currently being used or developed for reducing the effective acceleration sensitivity are considered. The techniques fall into three general categories: reduction of the acceleration sensitivity of the resonator; passive techniques that use compensating elements in the oscillator feedback loop, e.g. a second resonator or an acceleration sensitivity capacitor; and active acceleration compensation schemes that sense the acceleration and feedback a compensating signal to a tuning network.

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Reactions of a Vibrating Piezoelectric Crystal Plate to Externally Applied Forces

Cited by 11 publications

References 0 publications

Effect of transverse force on the performance of quartz resonator force sensors

Effect of transverse force on the performance of quartz resonator force sensors

Quartz resonator frequency shifts computed using the finite element method

The acceleration sensitivity of quartz crystal oscillators: a review

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