Free-Vibration Analysis of Piezoelectric-Quartz Double-Ended Tuning Fork
Date Issued
2010
Date
2010
Author(s)
Chang, Chun-Tse
Abstract
The purpose of this paper is to study the effect of piezoelectricity on the natural frequencies of DETF-type(double-ended tuning fork) resonator. which is made of ZYw+2°-cut quartz. This resonator is a tuning fork which consist of a pair of slender Euler beams and two proof masses at two ends of tuning fork. The tuning fork is driven by inputting alternative voltage into the electrodes coated on the surface of tuning fork. There are two different types of vibrational mode of tuning fork for the same order mode shape. That is “in-phase mode” and ”anti-phase mode”. We focus on the analysis of anti-phase mode.
The approach of this research is theoretical analysis, and using software ”Mathematica” to help us to calculate some detail compute. First of all, we neglect the effect of proof mass then construct a beam model to simulate tuning fork. Here we use “Euler beam” theory and “power series” method to describe the displacement and electric potential. Second, using Hamilton’s principle to derive the governing equation and boundary conditions of this problem. Finally, we can get characteristic solution and use boundary conditions to find out the resonant frequencies.
As to the natural-frequency evaluation of the entire DEFT resonator, we need, in advance, to establish the proper displacement model of the proof mass and derive its equations of motion and natural boundary conditions. Then we solve simultaneously the equations of motion of the tuning-fork beams and two proof masses together with their geometric and natural boundary conditions, and the continuity equations of displacement, slopes, moment at the interfaces, to get the natural frequencies of the flexible vibrations. Based on these obtained natural frequency of each mode, we can find out the corresponding mode shape, the electric field, and the strain field of the quartz tuning-fork beams. From the distributions and the relationships of the strain and electric fields, we can design the layout of the electrodes for efficiently driving the resonator into vibration at a particular natural frequency.
Subjects
quartz resonators
piezoelectricity
natural frequency(resonant frequency)
Type
thesis
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