Model for a Quartz-Crystal Tuning Fork Using Plate Spring Approximated to Torsion Spring Adopted at the Joint of the Arm and the Base

概要

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We developed a method for analyzing the frequency of a quartz-crystal tuning fork using plate spring approximation. In order to calculate the actual frequency of the tuning fork, we approximated the right half of the tuning fork as an $L$-shaped bar, of which the two beams, acting as the base and the arm undergo bending vibration, and a torsion spring at the joint of beam $A$ corresponding to the base and beam $B$ corresponding to the arm. Furthermore, we approximated torsion spring with torsion spring constant $R$ for a plate spring composed of a base. $R$ was expressed in terms of both the size and the bending stiffness of the tuning fork. We could obtain a series of equations for calculating the frequency of the tuning fork by the plate spring approximation and a convenient new frequency equation for a cantilever with a length $l_{2}+w_{1}/10$ by considering the bend of a plate spring. A comparison was made between the frequencies calculated by these methods and the experimental results.
Published by the Japan Society of Applied Physics through the Institute of Pure and Applied Physicsの論文
2003-05-15