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

Abstract

In the early 1970s, Basinski et a1 observed that, if two solid solutions of different solutes in a given solvent (copper or silver) had the same initial flow stress at a given temperature in the range 4-380 K, then they had the same activation volume. Moreover, two alloys based on the same solvent metal, which had the same initial flow stress and activation volume at a given temperature, would show the same temperature dependence of initial flow stress and activation volume throughout that range. These observations, which are known as the 'stress equivalence of solution hardening', have been shown to be readily accounted for in terms of the kink-pair formation model of solid-solution hardening.

Nanomechanical tuning forks fabricated using focused-ion-beam chemical vapor deposition

“…Tuning forks have generally been modeled by two methods: by using a beam (or beam-with-a-spring) model, [14][15][16] and by using a 2-degrees-of freedom model. [17][18][19] The beam model is appropriate for calculating resonant frequencies, and the 2-degrees-of-freedom model is appropriate for describing frequency responses.…”

Analysis of Change in Motional Capacitance of the Electrical Equivalent Circuit of Quartz-Crystal Tuning-Fork Tactile Sensor at Resonance by Combining Analytical Models for Elastic Foundation and L-Shaped Bar with Torsion Spring

“…As the torsion spring was approximately expressed by the plate spring, the torsion spring constant was given by 15) R ¼…”

Analysis of quality factor of quartz-crystal tuning forks using L-shaped bar model with torsion spring

“…19) However, an L-shaped bar model that consists of two bars indicating the right half of the tuning fork and a torsion spring at the joint of its arm and base beams gives precise values. 1) Figure 1(a) shows the configuration of the quartz-crystal tuning fork using a +2°X-cut quartz plate in which two arms vibrate in opposite directions. Figure 1 The Bernoulli-Euler beam theory, applied to the arm and base of the quartz-crystal tuning fork, is considered to be effective to describe the flexural displacement of the base and arm, because the calculated changes in the reciprocal motional capacitance of the quartz-crystal tuning fork tactile sensor using the flexural displacement of the base and arm of an Lshaped bar model and elastic foundation (before and after the sensor's base comes into contact with plastic materials) are in good agreement with the measured values at a resonant frequency of 32.5 kHz as shown in Fig.…”

“…The frequency of a quartz-crystal tuning fork was analyzed using an L-shaped bar model that depicted the right half of the tuning fork as two bars and also consisted of a torsion spring having the rotational Winkler coefficient R at the joint of the arm and base bars. 1) In this analysis, R was treated as a parameter for adjusting to match the frequency (32.768 kHz) of a quartz-crystal tuning fork. A formula for the dynamic capacitance of the quartz-crystal tuning fork at resonance was also derived using the L-shaped bar model.…”