Analysis of the natural frequency of a quartz double-end tuning fork with a new deformation model

The quartz double-end tuning fork is composed of two parallel slender beams with their ends fixed to the proof masses, both ends of which are clamped. The structure is made of a quartz wafer which is anisotropic in stiffness. In anti-phase mode the two slender parallel beams vibrate in opposite dire...

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Bibliographic Details
Published in:Journal of micromechanics and microengineering 2016-06, Vol.26 (6), p.65006-65019
Main Authors: Huang, Bo-Shiun, Chang-Chien, Wen-Tien, Hsieh, Fa-Hwa, Chou, Yuan-Fang, Chang, Chia-Ou
Format: Article
Language:English
Subjects:
Anisotropy
anti-phase mode
Beams (structural)
Deformation
Quartz
quartz crystal
resonance frequency
Stiffness
Tuning
tuning fork
Warpage
Warping
warping deformation
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Summary:The quartz double-end tuning fork is composed of two parallel slender beams with their ends fixed to the proof masses, both ends of which are clamped. The structure is made of a quartz wafer which is anisotropic in stiffness. In anti-phase mode the two slender parallel beams vibrate in opposite directions and can be modelled as an Euler beam. The twist moments caused by the slender beams on the proof mass make the cross-section of the proof mass deform into a warped surface. The objective of this research is to establish the warping deformation model so that we can build up the equation of motion for anisotropic stiffness by using Hamilton's principle and then perform theoretical analysis. The more realistic warping displacement leads the natural frequency closer to the true one. The purpose of the proof mass is to modulate the frequencies and mode shape of tuning fork beams. The advantage of anti-phase mode is that the centre of mass in unchanged during motion so that the system has a higher signal-to-noise ratio. The theoretically obtained frequency is compared with the experimental one and that obtained by the finite element method.
ISSN:0960-1317
1361-6439
DOI:10.1088/0960-1317/26/6/065006