## Abstract

We perform a theoretical analysis of the secondorder in-plane acceleration sensitivity of a Y-cut quartz thickness-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 perturbation 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 acceleration, the second-order frequency shift is nonzero and is quadratic in the acceleration. As the fourth-order nonlinear elastic constants of quartz have never been measured, we can only estimate the magnitude of the second-order frequency shift. For a particular case of interest, we find Δω/ω_{0}~10^{-18}, 10^{-16}, and 10^{-14} when the acceleration is 1, 10, and 100 g, respectively.

Original language | English (US) |
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Article number | 7185009 |

Pages (from-to) | 1421-1428 |

Number of pages | 8 |

Journal | IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control |

Volume | 62 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2015 |

Externally published | Yes |

### Bibliographical note

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