Effects of middle plane curvature on vibrations of a thickness-shear mode crystal resonator
نویسندگان
چکیده
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 sensitivity is also studied. It is shown that the middle plane curvature causes a frequency shift as large as 10 8 g 1 under a normal acceleration. These results have practical implications for the design of concave–convex and plano-convex resonators. 2006 Elsevier Ltd. All rights reserved.
منابع مشابه
Effect of Winkler Foundation on Radially Symmetric Vibrations of Bi-Directional FGM Non-Uniform Mindlin’s Circular Plate Subjected to In-Plane Peripheral Loading
An analysis has been presented of the effect of elastic foundation and uniform in-plane peripheral loading on the natural frequencies and mode shapes of circular plates of varying thickness exhibiting bi-directional functionally graded characteristics, on the basis of first order shear deformation theory. The material properties of the plate are varying following a power-law in both the radial ...
متن کاملDesign and Fabrication of a Quartz Crystal Resonator Used in a Thickness-Monitor Unit (TECHNICAL NOTES).
This paper deals with the design and fabrication of a quartz-crystal resonator used in a thickness-monitor unit, measuring film thickness in a film-depositing system. A purpose-grown quartz crystal is cut to form the desired wafer. Two gold electrodes are deposited on both surfaces of the wafer to provide electrical contacts. The resonance frequency of the resonator, at room temperature, and th...
متن کاملAn Integrated Analysis of Vibrations of Quartz Crystal Plates with the Mindlin Plate Theory for Resonator Design and Optimization
The high frequency vibrations of quartz crystal plates have been extensively studied for the design and optimization of resonators which work at the thickness-shear vibration mode with relatively high frequency in the RF range. Earlier research work started from the development of special plate equations required for the high frequency vibrations of quartz crystal plates by Mindlin, known as th...
متن کاملNonlinear Modeling and Investigating the Nonlinear Effects on Frequency Response of Silicon Bulk-mode Ring Resonator
This paper presents a nonlinear analytical model for micromechanical silicon ring resonators with bulk-mode vibrations. A distributed element model has been developed to describe the dynamic behavior of the micromechanical ring resonator. This model shows the nonlinear effects in a silicon ring resonator focusing on the effect of large amplitudes around the resonance frequency, material and ele...
متن کاملThe New Design and Simulation of an Optical Add Drop Filter Based On Hexagonal Photonic Crystal Single Ring Race Track Resonator
In this paper, using annular resonator we have designed an adding and dropping filter light based ontwo-dimensional photonic crystals. The shape of ring resonator filter adding and dropping that wehave proposed is Race Track. This filter has a hexagonal lattice structure of silicon bars withrefractive index 3/46 that is located in the context of air with refractive index 1. Transmissionefficien...
متن کامل