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Examines stress compensated quartz resonators having ultralinear frequency-temperature responses. Physical features of new linear and stress compensated cuts; Limitations existing in nonrotated Y-cut quartz plates; Resonance frequency equation for thickness-vibration modes in a thin ideal crystal plate.

When plane elastic waves are propagated in crystals, the three mechanical displacements corresponding to the three types of waves are mutually perpendicular and in the most general case none of them is normal or parallel to the wave front. However, when the waves are able to propagate in specific directions, these values show pure modes. This paper describes an investigation of the specific directions of the wave propagations in thin quartz crystal plates. Some experiments based on the calculated results are given and the measured values coincide well with the calculated ones. [ABSTRACT FROM AUTHOR]

When plane elastic waves propagate in specific directions in an anisotropic medium, they can satisfy the conditions of pure longitudinal and transverse plane elastic waves. The purpose of this paper is to find all the specific directions in which pure elastic waves propagate in thin LiTaO[sub 3] or LiNbO[sub 3] crystal plates. The result is that all the specific directions for pure plane elastic waves in thin LiTaO[sub 3] and LiNbO[sub 3] crystal plates have been thoroughly analysed. [ABSTRACT FROM AUTHOR]

By means of the clamped-free bar model, the impedance change of the tuning fork-type quartz resonator by the acoustic radiation resistance and the Stokes' resistance is studied theoretically and experimentally. From the analysis, it is found that the impedance change due to the acoustic radiation resistance and to the Stokes' resistance depends strongly on the shape of the resonator. It is found also that the impedance change by the acoustic radiation resistance cannot be neglected at the atmospheric pressure.

By using the clamped-free bar model, the impedance change of the tuning fork-type quartz resonator due to gas pressure was studied theoretically and experimentally. The drag force by the gas-kinetics and the mechanical loss energy caused on the crystal surface by the viscous friction are equated to the electric loss energy in the crystal resonator so that a new theoretical equation for the pressure-impedance characteristic was derived. The size dependence of the impedance change was derived theoretically and verified.

The resonant frequencies vs. gas pressure were studied experimentally and theoretically on the tuning-fork-type quartz resonators with rough surfaces operated in a gas with a flexural vibration. It is assumed that the gas flow at the boundary layer on a vibrating quartz tuning-fork resonator with rough surfaces is in transition from the laminar flow to a mixed fluid state that can be considered a turbulent flow. It is presumed that this turbulent flow increases the sur- face friction resistance. By extending the mixture length theory of the turbulent flow proposed by Prandtl, a phenomenological frequency formula is derived. From the experimental values, it is found that the theoretical equations for the frequency-gas pressure characteristics containing two empirical constants agree with the experimental results better than the previous equations. [ABSTRACT FROM AUTHOR]

This paper proposes a method of two dimenslonal analysis for the thickness-flexural vibration, where the one-dimensional finite-element method (FEM) is applied to the planar equation. This approach aims at application to the analysis of the flexural spurious vibrations of strip rectangular AT-cut plate often used in practice. The feature of the proposed method is that the two-dimensional coupled vibration can be analyzed by applying twice the one-dimensional FEM. in other words, the one-dimensional FEM is applied to the eigenmode guided by the X-edge, as well as to the resonant expression derived from the boundary condition on the Z'-edge. As a result, the considered matrix is reduced greatly in size compared to the direct analysis by the two-dimensional FEM. The result of calculation for the change of the resonant frequency due to the change of the Z'-edge ratio is compared to the result of experiment, and the usefulness of the proposed method is demonstrated. It is shown also that most of the spurious vibrations depending on the Z'-edge ratio are flexural vibrations, which is a new finding. [ABSTRACT FROM AUTHOR]