Theoretical Analysis of Natural Frequencies of Single-Crystal Quartz Accelerometers
Date Issued
2009
Date
2009
Author(s)
Chen, Ming-Tze
Abstract
The thesis is mainly to investigate the resonance frequencies of the (YXl)-88度 quartz beam and the (YXl)-88度 double-ended tuning fork quartz oscillator. First, the resonance frequencies of the quartz beam is analyzed in step one. Governing equations and boundary conditions are obtained by using Hamilton’s Principle and variational principle of mechanics. By applying the separation of variables method, we can derive the eigenequations. The eigenvalues can be obtained by using the analytic solutions. Thus, we can calculate the resonance frequencies of the quartz beam. The modes of the double-ended tuning fork quartz oscillator can be divided into the in-phase mode and the anti-phase mode. For the case of in-phase mode, the proof masses are simulated by using the assumption of Timoshenko beam, and the single beams are simulated by using the assumption of Euler beam. In anti-phase mode, we develop the assumption of anti-phase mode shapes of proof masses, and the single beams are simulated by using the assumption of Euler beam. The problem-solving processes of the in-phase mode and the anti-phase mode are the same as those of the former. Governing equations and boundary conditions are obtained using Hamilton’s Principle and variational principle of mechanics. By applying the separation of variables method, we can derive the eigenequations. The eigenvalues can be obtained by using the analytic solutions. Thus, we can calculate the resonance frequencies of the quartz tuning fork oscillator. The analytic solutions are closely consistent with the experimenting results. By using the same methods, we can analyze the resonance frequencies of the in-plane mode and the out-of-plane mode of the single ending tuning fork oscillator, and derive the theoretical sizes when the frequency is 32.768KHz.
Subjects
Quartz
Oscillator
Euler beam
Timoshenko beam
Natural frequency
Type
thesis
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