On the influence of a fabrication imperfection on the normal acceleration sensitivity of contoured quartz resonators with rectangular supports

It is shown that the normal acceleration sensitivity of contoured quartz resonators with rectangular supports vanishes when the centers of the mode shape and support rectangle coincide. This result is essentially a consequence of symmetry and applies to many other shapes. Since it is extremely difficult to realize this situation in practice, an analysis of the influence of an offset of the centers on the normal acceleration sensitivity is performed. The biasing deformation is determined by means of a variational approximation procedure using the variational principle with all natural conditions for anisotropic static flexure. The very important accompanying strains which vary quadratically across the thickness are determined recursively. The resulting flexural biasing states are used in the existing perturbation equation along with the equivalent trapped energy mode shapes of the contoured resonators to calculate the normal acceleration sensitivities. It is shown that for small offsets the acceleration sensitivity increases linearly with offsets and orientations for which this effect is minimized