## Abstract

A finite-element program incorporating R. D. Mindlin's first-order plate equations is developed. Calculations are performed for a miniature, third-overtone extensional, Z-cut resonator. Its frequency spectrum as a function of the mounting length and displacement mode shapes is discussed. The resonator motional resistances for different mounting lengths are measured. Normalized strain-energy ratios in the base area and tine area are computed and compared with the normalized motional resistance at various mounting lengths. Good correlations are found: the peaks in strain energy ratio correspond to peaks in motional resistance. Since the motional resistance is inversely proportional to the quality factor, Q, of the resonator, the strain-energy ratio in the base and tines (the supporting structure) could be used as a relative criterion for judging the Q of a certain resonator design.

Original language | English (US) |
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Pages (from-to) | 29-37 |

Number of pages | 9 |

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

Volume | 42 |

State | Published - Jun 1988 |

Event | Proceedings of the Annual Frequency Control Symposium - Baltimore, MD, USA Duration: Jun 1 1988 → Jun 3 1988 |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Electrical and Electronic Engineering