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An Estimate Of The Second-Order In-Plane Acceleration Sensitivity Of A Y-Cut Quartz Thickness-Shear Resonator, Huijing He, Jiashi Yang, John A. Kosinski

Department of Mechanical and Materials Engineering: Faculty Publications

We perform a theoretical analysis of the second-order in-plane acceleration sensitivity of a Y-cut quartz thick-ness-shear mode resonator. The second-order nonlinear theory of elasticity for anisotropic crystals is used to determine the biasing fields in the resonator under in-plane acceleration. The acceleration-induced frequency shift is determined from a per-turbation analysis based on the plate equations for small-amplitude vibrations superposed on a finite bias. We show that, whereas the first-order acceleration-induced frequency shift is zero for a structurally symmetric resonator under in-plane ac-celeration, the second-order frequency shift is nonzero and is quadratic in the acceleration. As the fourth-order nonlinear elastic constants …