Biomedical subjects
Publications and source records attributed to Roger Bourquin.
Temperature effects in gallium orthophosphate (GaPO4) vibrating beams are reported. In addition to the well-known, thickness-shear AT-cut, temperature-compensated cuts exist in GaPO4 for length extensional modes. Experimental evidence of a temperature-compensated cut in GaPO4 rectangular beam resonator vibrating in length extension is given.
The frequency of a flexural resonator and its frequency-temperature behavior usually are computed by Bernoulli's classical approximation. This approach is valid for beams with a large length-over-thickness-ratio. For shorter beams, the effects of shear stress and rotary inertia may play a significant role for temperature-compensated resonators. These effects have been taken into account for isotropic beams. The aim of this paper is to discuss the extension of the shear coefficient in the case of an anisotropic material and to compute the frequency-temperature characteristic of an (XYt)theta cut resonator when the shear stress and the rotary inertia have been taken into account. Comparisons between the classical approximation and this treatment are given for quartz. Furthermore, the numerical predictions obtained by means of different sets of data available for thermal sensitivities of elastic coefficients are compared.
Flexural modes are the basic vibrating mode of tuning forks used in quartz wrist watches; they also can be used as the basis for sensors. Very little work, if any, has been done for vibrating beam resonators in GaPO4. In this paper, the possibility of temperature-compensated cuts in GaPO4 is investigated for length-extensional and flexural vibrating modes. A theoretical investigation of rectangular cross-section GaPO4 vibrating beam resonators is accomplished by analytical methods. Modeling temperature effect is achieved by the approximate but classical method in which the effective elastic constants, beam dimensions, and crystal mass density are varied as a function of temperature. Temperature-compensated cuts are given in GaPO4 for length-extensional and flexural modes. Some temperature-compensated cuts of GaPO4 exhibit inversion points at high temperatures.
It has been shown in earlier works that the amplitude-frequency effect [also called isochronism defect (ID) or anisochronism] could be a limitation factor on ultrastable oscillators. Theoretical studies based on the nonlinear theory of piezoelectricity have already been developed to explain the amplitude-frequency effect. So, it is possible to estimate the dependence of the ID versus various parameters of the resonator design (overtone rank, radius of curvature, electrodes diameter, etc.). However, because of the lack of available fourth-order elastic coefficients, it is not possible to predict the ID of any resonant frequency of a given trapped energy resonator. To tentatively find orientations of plates exhibiting a quasi-null ID, we have realized electroded resonators with different orientations and curvatures. We present results that verify, particularly, the R(-1/2) dependence of the amplitude-frequency effect versus radius of curvature. Moreover, we show that the ID can be positive or negative, that it can vary from one orientation to other one of about one order of magnitude, and that there exists a thermal compensated mode for which the amplitude-frequency effect is null.