## Abstract

In a previous paper by the authors, three-dimensional linear field equations for small vibrations superposed on thermally induced deformations by steady and uniform temperature changes were derived from the nonlinear field equations of thermoelasticity in Lagrangian formulation. From the solutions of these equations for the simple-thickness vibrations and measurements by R. Bechmann, et al. (1963) for various doubly rotated quartz plates, values of the first temperature derivatives and effective second temperature derivatives of quartz were calculated. In this study, the previous work is extended to include the third-order perturbations so that values of the effective third temperature derivatives are obtained for quartz. By regrouping the terms in the incremental stress-strain-temperature relations, certain expressions in terms of the elastic stiffnesses, temperature derivatives, and thermal expansion coefficients can be identified as having similar significance as the temperature coefficients of C//p //q defined by R. Bechmann.

Original language | English (US) |
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Pages (from-to) | 164-175 |

Number of pages | 12 |

Journal | Proceedings of the Annual IEEE International Frequency Control Symposium |

State | Published - 1984 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Electrical and Electronic Engineering