FREQUENCY-TEMPERATURE CHARACTERISTIC OF FLEXURAL RESONATORS USING THE MODEL OF TIMOSHENKO

摘要

The classical Bernoulli's approximation is usually used to compute the frequency of a flexural resonator (like tuning fork resonator) and to determine its frequencytemperature behaviour. This approximation is valid for beams with a large length/width ratio. For short beams, the effects of shear stress and rotatory inertia may play a significant role for temperature compensated resonators. These effects have been taken into account by Timoshenko for the prediction of frequency of resonance of isotropic beam. The aim of this paper is to discuss the extension of Timoshenko's shear coefficient in the case of an anisotropic material and to compute the frequencytemperature characteristic of a X + q cut resonator when the shear stress and the rotatory inertia have been taken into account. Comparisons between the classical (approximated) and the present "exact" treatments are given for quartz. Furthermore, we compare the numerical predictions obtained by using the different sets of data available for thermal sensitivities of elastic coefficients.