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Nonlinear finite element modeling of quartz crystal resonators.

机译：石英晶体谐振器的非线性有限元建模。

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摘要

In order to facilitate the design of quartz resonators, the overall goal of the current work was to develop an accurate three-dimensional finite element model for the anisotropic frequency response of quartz. The model was based on the linear incremental equations for superimposed small vibrations onto nonlinear thermoelastic stressed media. The frequency response of the model was benchmarked to experimental data from quartz pressure sensors with temperature ranging from 50 °C to 200 °C and pressure from 14 psi to 20,000 psi. This direct finite element approach for frequency response at such high pressure had not been previously examined in literature.;The normalized frequency response to the change in external pressure from 14 psi to 20,000 psi matched very well with experimental data for lower temperatures, having a maximum deviation of only 7.5% at 20,000 psi when assuming constant 50 °C temperature. However, the same deviation grew to 25.7% assuming a higher 200 °C constant temperature. Similarly, the temperature-frequency response at constant pressure from 50 °C to 200 °C matched the experimental trend well for lower pressures, but this agreement deteriorated as pressure increased.;The nature of the observed frequency deviations suggests that changes in the third-order elastic constants with temperature, a quartz material definition that is not currently available in literature, could play a significant role in accurately modeling the frequency response at such conditions, and that the lack of such properties is the primary source of the error in both temperature and pressure response. This hypothesis was tested by using a novel method of giving the third-order elastic constants linear temperature dependence based on a single scalar parameter, for which a specific value was empirically derived for the AT-Cut quartz pressure sensor studied. Specifically, modeling a scalar decrease in magnitude of about 0.0775% per °C in the third-order elastic coefficients was shown to decrease the error of the simulation at the highest temperature and pressure from 25.7% to 4.0%, and this improvement was mirrored throughout the range of temperatures and pressures tested. Furthermore, knowing the expected benefit of implementing the third-order elastic coefficients as functions of temperature should aid future researchers in deciding if defining their full anisotropic temperature derivatives is practical, and relevant possibilities for such a study are given.
机译：为了简化石英谐振器的设计，当前工作的总体目标是为石英的各向异性频率响应建立一个精确的三维有限元模型。该模型基于线性增量方程，用于将小振动叠加到非线性热弹性应力介质上。该模型的频率响应以石英压力传感器的实验数据为基准，温度范围为50°C至200°C，压力范围为14 psi至20,000 psi。这种在如此高的压力下直接进行频率响应的直接有限元方法以前没有在文献中进行过研究。对从14 psi到20,000 psi的外部压力变化的归一化频率响应与较低温度的实验数据非常吻合，最大假设温度恒定为50°C，在20,000 psi下的偏差仅为7.5％。但是，假设更高的200°C恒定温度，相同的偏差会增加到25.7％。同样，在50°C至200°C的恒定压力下，温度-频率响应与较低压力下的实验趋势非常吻合，但是随着压力的增加，这种一致性恶化。;观察到的频率偏差的性质表明，随温度变化的阶数弹性常数，目前在文献中尚不可用的石英材料定义可以在精确模拟这种条件下的频率响应中发挥重要作用，并且缺乏这种特性是两个温度下误差的主要来源和压力响应。通过使用一种基于单个标量参数给出三阶弹性常数线性温度依赖性的新颖方法，对该假设进行了检验，为此，根据经验得出了研究的AT-Cut石英压力传感器的特定值。具体而言，对三阶弹性系数每℃大约减少0.0775％的数量级建模表明，将在最高温度和压力下的模拟误差从25.7％降低到4.0％，并且这种改善在整个过程中都得到了反映。测试的温度和压力范围。此外，了解将三阶弹性系数实现为温度函数的预期好处将有助于未来的研究人员确定定义其完整的各向异性温度导数是否可行，并为此类研究提供了相关的可能性。

著录项

  • 作者

    Beerwinkle, Austin Dale.;

  • 作者单位

    Oklahoma State University.;

  • 授予单位 Oklahoma State University.;
  • 学科 Geotechnology.;Engineering Materials Science.;Engineering Mechanical.
  • 学位 M.S.
  • 年度 2011
  • 页码 81 p.
  • 总页数 81
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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