Yong Y K, Zhang Z
Dept. of Civil and Environ. Eng., Rutgers Univ., Piscataway, NJ.
IEEE Trans Ultrason Ferroelectr Freq Control. 1994;41(5):685-93. doi: 10.1109/58.308504.
Finite element matrix equations, derived from two-dimensional piezoelectric high frequency plate theory are solved to study the vibrational behavior of the third overtone of thickness shear in square and circular SC-cut quartz resonators. The mass-loading and electric effects of electrodes are included. A perturbation method which reduces the memory requirements and computational time significantly is employed to calculate the piezoelectric resonant frequencies. A new storage scheme is introduced which reduces memory requirements for mass matrix by about 90% over that of the envelope storage scheme. Substructure techniques are used in eigenvalue calculation to save storage. Resonant frequency and the mode shapes of the harmonic third overtone thickness shear vibrations for square and circular plates are calculated. A predominant third overtone thickness shear displacement, coupled with the third overtone of thickness stretch and thickness twist, is observed. Weak coupling between the third order thickness shear displacement and the zeroth-, first-, and second-order displacements is noted. The magnitudes of the lower order displacements are found to be about two orders smaller than that of the third overtone thickness shear displacement.
求解由二维压电高频板理论推导得到的有限元矩阵方程，以研究方形和圆形SC切石英谐振器中厚度剪切振动第三泛音的振动行为。其中考虑了电极的质量负载和电学效应。采用一种能显著降低内存需求和计算时间的微扰方法来计算压电谐振频率。引入了一种新的存储方案，与包络存储方案相比，该方案将质量矩阵的内存需求减少了约90%。在特征值计算中使用子结构技术以节省存储空间。计算了方形和圆形板的谐振频率以及谐波第三泛音厚度剪切振动的振型。观察到一个占主导地位的第三泛音厚度剪切位移，它与厚度拉伸和厚度扭转的第三泛音耦合。注意到三阶厚度剪切位移与零阶、一阶和二阶位移之间存在弱耦合。发现低阶位移的量级比第三泛音厚度剪切位移的量级小约两个数量级。
