Frequency shifts in plate crystal resonators induced by electric, magnetic, or mechanical fields in surface films

Liu, Nan; Yang, Jiashi; Hu, Yuantai; Chen, Xuedong; Jiang, Wei

doi:10.1109/tuffc.2011.2122

Cited by 2 publications

(1 citation statement)

References 25 publications

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“…He revealed that the e ect of piezoelectricity on force-frequency coe cient of incomplete quartz resonating disk is about 7 percent when the force azimuth angle is zero [17]. In addition to Mindlin procedure, other analytical methods like perturbation method, developed by Tiersten [18], and full numerical methods are used to determine frequency shift in quartz resonators due to external perturbations [14,[19][20][21][22][23]. The accuracy of these methods is acceptable, but they are complicated and time consuming.…”

Section: Introductionmentioning

confidence: 99%

Eect of anisotropy and piezoelectricity on the force-frequency coecient of AT-cut quartz crystals

2016

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Abstract. A clear understanding of force-frequency e ect is essential for enhancing the accuracy of quartz crystal resonators and sensors. Several analytical models have been developed to predict the frequency change of piezoelectric crystals like quartz due to forcefrequency e ect. According to these models, frequency change is due to initial mechanical stresses caused by the application of diametrical forces. Usually, the anisotropy and piezoelectricity of quartz are neglected in determination of stress bias and in force-frequency equation. In this research, we quanti ed the e ect of anisotropy and piezoelectricity of ATcut quartz on the force-frequency coe cient. To this end, besides using the mathematical models, a nite element code, based on linear and nonlinear Lagrangian formulations, was developed. The FEM showed more reliable results than di erent analytical approaches. We found that the force-frequency coe cient is more sensitive to the anisotropy than to the piezoelectricity of quartz. By considering the anisotropy, the standard error of the force-frequency model decreased from 12.4 E-15 (ms/N) to 5.75 E-15 (ms/N). On the other hand, anisotropy can modify the shape of force-frequency curve at force azimuth angles close to 0 .

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Section: Introductionmentioning

confidence: 99%

Eect of anisotropy and piezoelectricity on the force-frequency coecient of AT-cut quartz crystals

2016

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Extensional Waves in a Sandwich Plate With Interface Slip

Jin

Chen

Yang

2015

Journal of Vibration and Acoustics

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The two-dimensional (2D) equations for thin elastic plates are used to study extensional motions of a sandwich plate with weak interfaces. The interfaces are governed by the shear-slip model that possesses interface elasticity and allows for a discontinuity of the tangential displacements at the interfaces. Equations for the individual layers of the sandwich plate are coupled by the interface conditions. Through a procedure initiated by Mindlin, the layer equations can be written into equations for the collective motion of the layers representing the extensional motion of the sandwich plate, and equations for the relative motions of the layers with respect to each other representing the symmetric thickness-shear motion of the sandwich plate. The use of plate equations results in relatively simpler models compared to the equations of three-dimensional (3D) elasticity. Solutions to a few useful problems are presented. These include the propagation of straight-crested waves in an unbounded plate with weak interfaces, the reflection of extensional waves at the joint between a perfectly bonded sandwich plate and a sandwich plate with weak interfaces, and the vibration of a finite sandwich plate with weak interfaces.

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Frequency shifts in plate crystal resonators induced by electric, magnetic, or mechanical fields in surface films

Cited by 2 publications

References 25 publications

Eect of anisotropy and piezoelectricity on the force-frequency coecient of AT-cut quartz crystals

Eect of anisotropy and piezoelectricity on the force-frequency coecient of AT-cut quartz crystals

Extensional Waves in a Sandwich Plate With Interface Slip

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