An analysis of the normal acceleration sensitivity of contoured quartz resonators stiffened by identical top and bottom quartz cover plates supported by clips

A stiffened structure in which the active biconvex quartz resonator is sandwiched between identical top and bottom quartz cover plates to which it is attached by means of small sidewalls around the periphery is considered. The mounting clips are attached to the cover plates without touching the active plate. An analysis of the normal acceleration sensitivity of this configuration is performed. The variational principle for anisotropic static flexure in which all conditions arise as natural conditions is extended to include the influence of the cover plates, the active region, and the clips. The calculations reveal that increasing the thickness of the cover plates relative to the active plate reduces the normal acceleration sensitivity arising from either a misplacement of a clip or a mispositioning of the center of the mode shape. The influence of symmetric holes in the cover plates is included in the calculations. Results are presented for a range of thicknesses of cover plates relative to the active plate and hole size