The increase in the in-plane acceleration sensitivity of the plano-convex resonator due to its thickness asymmetry

An analysis of the degradation in the in-plane acceleration sensitivity that arises from the contour being on one side only is performed. Under in-plane acceleration, the single contour causes a state of flexure and asymmetric shear to exist in the resonator plate. The flexural biasing deformation is determined by means of a variational approximation procedure. The shearing stresses varying through the thickness and accompanying strains are determined recursively. The resulting biasing states are employed in the existing perturbation equation along with the equivalent trapped energy mode shapes of the contoured resonators to calculate the degradation in the in-plane acceleration sensitivity caused by the loss of symmetry of the plano-convex resonator. The calculated results show that the in-plane sensitivity increases with decreasing radius of curvature and lies in the range of a few parts in 10¹² per g