Wang Zhe, Huang Bin, Guo Yan, Jiang Yanan, Khan Asif
Zhejiang-Italy Joint Lab for Smart Materials and Advanced Structures, Faculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo 315211, China.
College of Science & Technology, Ningbo University, Ningbo 315300, China.
Sensors (Basel). 2024 Oct 18;24(20):6707. doi: 10.3390/s24206707.
The primary objective of modal identification for variable thickness quartz plates is to ascertain their dominant operating mode, which is essential for examining the vibration of beveled quartz resonators. These beveled resonators are plate structures with varying thicknesses. While the beveling process mitigates some spurious modes, it still presents challenges for modal identification. In this work, we introduce a modal identification technique based on the energy method. When a plate with variable thickness is in a resonant state of thickness-shear vibration, the proportions of strain energy and kinetic energy associated with the thickness-shear mode in the total energy reach their peak values. Near this frequency, their proportions are the highest, aiding in identifying the dominant mode. Our research was based on the Mindlin plate theory, and appropriate modal truncation were conducted by retaining three modes for the coupled vibration analysis. The governing equation of the coupled vibration was solved for eigenvalue problem, and the modal energy proportions were calculated based on the determined modal displacement and frequency. Finally, we computed the eigenvalue problems at different beveling time, as well as the modal energies associated with each mode. By calculating the energy proportions, we could clearly identify the dominant mode at each frequency. Our proposed method can effectively assist engineers in identifying vibration modes, facilitating the design and optimization of variable thickness quartz resonators for sensing applications.
可变厚度石英板模态识别的主要目标是确定其主导工作模式，这对于研究斜角石英谐振器的振动至关重要。这些斜角谐振器是具有不同厚度的平板结构。虽然倒角工艺减轻了一些杂散模式，但它仍然给模态识别带来挑战。在这项工作中，我们引入了一种基于能量法的模态识别技术。当可变厚度平板处于厚度剪切振动的共振状态时，与厚度剪切模式相关的应变能和动能在总能量中的比例达到峰值。在该频率附近，它们的比例最高，有助于识别主导模式。我们的研究基于Mindlin板理论，并通过保留三种模式进行耦合振动分析来进行适当的模态截断。求解耦合振动的控制方程以得到特征值问题，并根据确定的模态位移和频率计算模态能量比例。最后，我们计算了不同倒角时间的特征值问题以及与每个模式相关的模态能量。通过计算能量比例，我们可以清楚地识别每个频率下的主导模式。我们提出的方法可以有效地帮助工程师识别振动模式，促进用于传感应用的可变厚度石英谐振器的设计和优化。
