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Full-Text Articles in Mechanical Engineering
An Estimate Of The Second-Order In-Plane Acceleration Sensitivity Of A Y-Cut Quartz Thickness-Shear Resonator, Huijing He, Jiashi Yang, John A. Kosinski
An Estimate Of The Second-Order In-Plane Acceleration Sensitivity Of A Y-Cut Quartz Thickness-Shear Resonator, Huijing He, Jiashi Yang, John A. Kosinski
Department of Mechanical and Materials Engineering: Faculty Publications
We perform a theoretical analysis of the second-order in-plane acceleration sensitivity of a Y-cut quartz thick-ness-shear mode resonator. The second-order nonlinear theory of elasticity for anisotropic crystals is used to determine the biasing fields in the resonator under in-plane acceleration. The acceleration-induced frequency shift is determined from a per-turbation analysis based on the plate equations for small-amplitude vibrations superposed on a finite bias. We show that, whereas the first-order acceleration-induced frequency shift is zero for a structurally symmetric resonator under in-plane ac-celeration, the second-order frequency shift is nonzero and is quadratic in the acceleration. As the fourth-order nonlinear elastic constants …
Analysis Of Electrically-Forced Vibrations Of Piezoelectric Mesa Resonators, Huijing He, Guo-Quan Nie, Jin-Xi Liu, Jiashi Yang
Analysis Of Electrically-Forced Vibrations Of Piezoelectric Mesa Resonators, Huijing He, Guo-Quan Nie, Jin-Xi Liu, Jiashi Yang
Department of Mechanical and 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
Effects Of Mode Coupling On The Admittance Of An At-Cut Quartz Thickness-Shear Resonator, Huijing He, Jiashi Yang, Wei-Ping Zhang, Ji Wang
Department of Mechanical and 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 length/thickness ratio, …
Energy Trapping Of Thickness-Shear And Thickness-Twist Modes In A Partially Electroded At-Cut Quartz Resonator, Huijing He, Guoquan Nie, Jinxi Liu, Jiashi Yang
Energy Trapping Of Thickness-Shear And Thickness-Twist Modes In A Partially Electroded At-Cut Quartz Resonator, Huijing He, Guoquan Nie, Jinxi Liu, Jiashi Yang
Department of Mechanical and Materials Engineering: Faculty Publications
The thickness-shear and thickness-twist vibrations of a finite and partially electroded AT-cut quartz resonator are investigated. 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 free vibration resonant frequencies, mode shapes, and energy trapping are calculated and examined.
Effects Of A Mass Layer With Gradually Varying Thickness On A Quartz Crystal Microbalance, Nan Liu, Jiashi Yang, Weiqiu Chen
Effects Of A Mass Layer With Gradually Varying Thickness On A Quartz Crystal Microbalance, Nan Liu, Jiashi Yang, Weiqiu Chen
Department of Mechanical and Materials Engineering: Faculty Publications
We study the effects of the nonuniform thickness of a thin mass layer on a quartz crystal microbalance. A theoretical analysis is performed on thickness-shear vibration of an AT-cut quartz plate with a nonuniform mass layer. Mindlin’s two-dimensional equation for thickness-shear vibration of a quartz plate is used. Free vibration frequencies and modes are obtained. The effects of the mass layer nonuniformity are examined. It is shown that resonant frequencies and energy trapping of thickness-shear modes are sensitive to mass layer nonuniformity.
Effects Of Middle Plane Curvature On Vibrations Of A Thickness-Shear Mode Crystal Resonator, J. S. Yang, Xiaomeng Yang, Joseph A. Turner, John A. Kosinski, Robert A. Pastore, Weiping Zhang
Effects Of Middle Plane Curvature On Vibrations Of A Thickness-Shear Mode Crystal Resonator, J. S. Yang, Xiaomeng Yang, Joseph A. Turner, John A. Kosinski, Robert A. Pastore, Weiping Zhang
Department of Engineering Mechanics: Faculty Publications
We study the effects of a small curvature of the middle plane of a thickness-shear mode crystal plate resonator on its vibration frequencies, modes and acceleration sensitivity. Two-dimensional equations for coupled thickness-shear, flexural and extensional vibrations of a shallow shell are used. The equations are simplified to a single equation for thickness-shear, and two equations for coupled thickness-shear and extension. Equations with different levels of coupling are used to study vibrations of rotated Y-cut quartz and langasite resonators. The influence of the middle plane curvature and coupling to extension is examined. The effect of middle plane curvature on normal acceleration …