A mechanical isolation of a bending resonator

In a vacuum (pressure less than 0.1 mbar), the quality factor (Q-factor) of a crystal is determined by the clamping loss, the inner friction of the material and by surface effects. Concerning the first of these damping mechanisms much work has been executed on the clamping loss of quartz tuning forks, which are applied in high quality time bases. Weisbord suggested for quartz devices the addition of a blocking mass, which compensates at the clamping the moment and the force in the flexural mode of a beam. Since Weisbord did not consider the dynamic interaction between the resonant beam and the blocking masses the coupling was not eliminated.In a more general approach a new model was developed here in which unlike to Weisbord's analysis, the full dynamic interaction with the clamp was taken into consideration. First, a single blocking mass for bending waves is described. Second, the behaviour of a beam, clamped between two blocking masses and vibrating in its bending mode is analytically analysed. The result is the theoretical prediction of a low loss resonant beam with blocking masses. The presented new resonator is a very promising step towards the realization of quality factors much higher than currently achieved with bending resonators.