EerNisse E P
Quartzdyne, Inc, Salt Lake City, UT 84123, USA.
IEEE Trans Ultrason Ferroelectr Freq Control. 2001 Sep;48(5):1351-61. doi: 10.1109/58.949744.
It is the intent of this work to provide a working resource for calculating all three mode families of a doubly rotated, contoured quartz resonator. It is shown that the theoretical development of Stevens and Tiersten [1] can be used for this purpose. Their approach uses a transformation of the mechanical displacement vector to the eigenvector triad of the pure thickness solution. The solution methodology here reorganizes the transformation matrix Q in their formulation to calculate the other two mode families. Calculations compare well with experimental results for the three mode families of an SC-cut crystal and an FC-cut crystal and with published calculations for the SBTC-cut mode family with major displacement along the x3 blank axis. The key constants for the SC-cut are presented for workers to use in the future. In addition, the equations of motion and boundary conditions are derived for the two additional mode families using assumptions parallel to those used by Stevens and Tiersten [1]. Calculations with these equations are presented for completeness to support the present conclusions by showing the equivalence of either simply reorganizing the Q matrix or using separate equations for each of the three mode families.
这项工作的目的是提供一个计算双旋转、异形石英谐振器所有三个模式族的实用资源。结果表明，史蒂文斯（Stevens）和蒂尔斯滕（Tiersten）[1]的理论发展可用于此目的。他们的方法是将机械位移矢量变换为纯厚度解的特征向量三元组。这里的求解方法重新组织了他们公式中的变换矩阵Q，以计算另外两个模式族。对于SC切型晶体和FC切型晶体的三个模式族，计算结果与实验结果以及沿x3空白轴有主要位移的SBTC切型模式族的已发表计算结果进行了很好的比较。给出了SC切型的关键常数，供研究人员今后使用。此外，使用与史蒂文斯和蒂尔斯滕[1]所使用的假设平行的假设，推导了另外两个模式族的运动方程和边界条件。为了完整起见，给出了使用这些方程的计算结果，通过展示简单地重新组织Q矩阵或为三个模式族中的每一个使用单独方程的等效性来支持当前结论。
