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Thickness-Shear And Thickness-Twist Vibrations Of Circular At-Cut Quartz Resonators, Huijing He, Jiashi Yang, Qing Jiang Jun 2013

Thickness-Shear And Thickness-Twist Vibrations Of Circular At-Cut Quartz Resonators, Huijing He, Jiashi Yang, Qing Jiang

Mechanical & Materials Engineering Faculty Publications

Exact solutions for free vibration frequencies and modes are obtained for thickness-shear and thickness-twist vibrations of unelectroded circular AT-cut quartz plates governed by the two-dimensional scalar differential equation derived by Tiersten and Smythe. Comparisons are made with experimental results and the widely-used perturbation solution by Tiersten and Smythe under the assumption of weak in-plane anisotropy. Our solution is found to be much closer to the experimental results than the perturbation solution . For the frequency of the fundamental thickness- shear mode, the error of the perturbation method is 0.4549%, significant in resonator applications.


Thickness-Shear Vibration Of A Rectangular Quartz Plate With Partial Electrodes, Huijing He, Jiashi Yang, John A. Kosinski, Ji Wang Apr 2013

Thickness-Shear Vibration Of A Rectangular Quartz Plate With Partial Electrodes, Huijing He, Jiashi Yang, John A. Kosinski, Ji Wang

Mechanical & Materials Engineering Faculty Publications

We study free vibration of a thickness-shear mode crystal resonator of AT-cut quartz. The resonator is a rectangular plate partially and symmetrically electroded at the center with rectangular electrodes. A single-mode, three-dimensional equation governing the thickness-shear displacement is used. A Fourier series solution is obtained. Numerical results calculated from the series show that there exist trapped thickness-shear modes whose vibration is mainly under the electrodes and decays rapidly outside the electrodes. The effects of the electrode size and thickness on the trapped modes are examined.


Analysis Of Electrically-Forced Vibrations Of Piezoelectric Mesa Resonators, Huijing He, Guo-Quan Nie, Jin-Xi Liu, Jiashi Yang Jan 2013

Analysis Of Electrically-Forced Vibrations Of Piezoelectric Mesa Resonators, Huijing He, Guo-Quan Nie, Jin-Xi Liu, Jiashi Yang

Mechanical & Materials Engineering Faculty Publications

We study the electrically forced thickness-shear and thickness-twist vibrations of stepped thickness piezoelectric plate mesa resonators made of polarized ceramics or 6-mm class crystals. A theoretical analysis based on the theory of piezoelectricity is performed, and an analytical solution is obtained using the trigonometric series. The electrical admittance, resonant frequencies, and mode shapes are calculated, and strong energy trapping of the modes is observed. Their dependence on the geometric parameters of the resonator is also examined.


Effects Of Mode Coupling On The Admittance Of An At-Cut Quartz Thickness-Shear Resonator, Huijing He, Jiashi Yang, Wei-Ping Zhang, Ji Wang Jan 2013

Effects Of Mode Coupling On The Admittance Of An At-Cut Quartz Thickness-Shear Resonator, Huijing He, Jiashi Yang, Wei-Ping Zhang, Ji Wang

Mechanical & Materials Engineering Faculty Publications

We study the effects of couplings to flexure and face-shear modes on the admittance of an AT-cut quartz plate thickness-shear mode resonator. Mindlin’s two-dimensional equations for piezoelectric plates are employed. Electrically forced vibration solutions are obtained for three cases: pure thickness-shear mode alone; two coupled modes of thickness shear and flexure; and three coupled modes of thickness shear, flexure, and face shear. Admittance is calculated and its dependence on the driving frequency and the length/thickness ratio of the resonator is examined. Results show that near the thickness-shear resonance, admittance assumes maxima, and that for certain values of the ...


Analysis Of A Monolithic Crystal Plate Acoustic Wave Filter, Huijing He May 2011

Analysis Of A Monolithic Crystal Plate Acoustic Wave Filter, Huijing He

Mechanical & Materials Engineering Faculty Publications

We study thickness–shear and thickness–twist vibrations of a finite, monolithic, AT-cut quartz plate crystal filter with two pairs of electrodes. The equations of anisotropic elasticity are used with the omission of the small elastic constant c56 . An analytical solution is obtained using Fourier series from which the res-onant frequencies, mode shapes, and the vibration confinement due to the electrode inertia are calculated and examined.


Piezoelectromagnetic Waves In A Ceramic Plate Between Two Ceramic Half-Spaces, S. N. Jiang, Q. Jiang, X. F. Li, S. H. Guo, H. G. Zhou, J. S. Chang Jan 2006

Piezoelectromagnetic Waves In A Ceramic Plate Between Two Ceramic Half-Spaces, S. N. Jiang, Q. Jiang, X. F. Li, S. H. Guo, H. G. Zhou, J. S. Chang

Mechanical & Materials Engineering Faculty Publications

We analyze the propagation of piezoelectromagnetic waves guided by a plate of polarized ceramics between two ceramic half-spaces. An exact dispersion relation is obtained, which reduces to a few known elastic, electromagnetic, and quasistatic piezoelectric wave solutions in the literature as special cases. Numerical solutions to the equation that determines the dispersion relation show the existence of guided waves. The results are useful for acoustic wave and microwave devices.