Natural Frequency Analysis of Axially-Loaded on the Double-Ended Tuning Fork Piezoelectric-Quartz Resonator

The thesis mainly studied about a Z-cut2° double-ended tuning fork quartz resonator, analyzing the impact of the pre-stressed force and piezoelectric effect on a natural frequency, for the sake of approaching the real situation and application of resonance frequency change. The double-ended tuning fork type quartz resonator is composed of a pair of slender Euler beams and two proof masses located at the two ends of the resonator. There are two vibration modes of the tuning fork for the same order mode shape that is in-phase mode and anti-phase mode. The thesis is mainly focus on the analysis of the anti-phase mode, Before performing the analysis of the whole quartz resonator. First, it doesn''t consider the free vibration behavior of the mass effect on quartz single beam. Simulate single beam deformation by Euler beam theory, using the Hamilton''s principle building the governing equation and the boundary condition of the single beam model, and to use the “Mathematica” software to solve the frequency-related characteristic equation numerically, and to calculate the natural frequencies of mode sharps.
For two ends of the proof masses building the warping model which is according to the moment that caused by the anti-phase mode from the tuning fork to the proof masses； Assuming the coupling structure as an elastic body, discussing the free vibration to each structure, By Hamilton''s principle getting the governing equation and the boundary condition. For coupling, to base on the single beam and proof mass of geometric boundary conditions at interface, obtaining the natural frequencies of each mode for the double ended tuning fork type quartz oscillator, and to acquire the relationship between the pre-stressed force and the natural frequencies variation.