An analysis of the in-plane acceleration sensitivity of contoured quartz resonators with rectangular supports

It is shown that the resultant in-plane acceleration sensitivity of contoured quartz resonators symmetrically supported along rectangular edges always vanishes. This result is essentially a consequence of symmetry and applies to any shape for which the support system is symmetric with respect to the center of the mode shape. When the active plate is supported on one side only, a state of flexure is induced in the resonator which degrades the in-plane sensitivity. This emphasizes the importance of a symmetric support system to achieve low acceleration sensitivities. The extensional and induced in-plane flexural biasing deformations are determined by means of the variational approximation procedure using the variational principles in which all conditions appear as natural conditions. The resulting biasing states are used in a perturbation equation along with the mode shapes of the contoured resonators to calculate the non-vanishing acceleration sensitivities