Identification of Vibration Modes of Quartz Crystal Plates with Proportion of Strain and Kinetic Energies

IF 0.8 4区 工程技术 Q4 ACOUSTICS International Journal of Acoustics and Vibration Pub Date : 2020-09-30 DOI:10.20855/ijav.2020.25.31671
Qi Huang, R. Wu, Li-hong Wang, Longtao Xie, Jianke Du, T. Ma, Ji Wang
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引用次数: 1

Abstract

For the design of quartz crystal resonators, finding and determining the vibration modes have always been very important and cumbersome. Vibration modes are usually identified through plotting displacement patterns of each coupled modes and making comparisons. Over the years, there is not much improvement in the identification procedure while tremendous efforts have been made in refining the equations of the Mindlin plate theory to obtain more accurate results, such as the adoption of the Finite Element Method (FEM) by implementing the high-order Mindlin plate equations for efficient analysis. However, due to the old fashioned mode identification method, the FEM application is still inadequate and cannot be fully automated for this purpose. To have this situation improved, a method using the proportions of strain and kinetic energies to characterize the energy level of each vibration mode is proposed. With solutions of displacements, the energy distribution of each vibration mode is calculated and the mode with the highest energy concentration at a specific frequency is designated as the dominant mode. The results have been validated with the traditional approach by plotting mode shapes at each frequency. Clearly, this energy approach will be advantageous with the FEM analysis for vibration mode identification automatically.
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用应变和动能的比例识别石英晶体板的振动模式
在石英晶体谐振器的设计中,振动模态的寻找和确定一直是一个非常重要和繁琐的问题。通常通过绘制每个耦合模态的位移模式并进行比较来识别振动模态。多年来,辨识程序并没有太大的改进,但为了得到更精确的结果,人们在完善Mindlin板理论方程方面做了大量的努力,例如采用有限元法实现高阶Mindlin板方程,以进行有效的分析。然而,由于传统的模态识别方法,有限元法的应用仍然不足,不能完全自动化。为了改善这种情况,提出了一种利用应变和动能的比例来表征各振动模态能级的方法。根据位移解,计算各振型的能量分布,指定某一特定频率下能量集中最高的振型为主导振型。用传统方法在各频率处绘制模态振型,验证了所得结果。显然,这种能量法将有利于有限元分析的振动模态自动识别。
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来源期刊
International Journal of Acoustics and Vibration
International Journal of Acoustics and Vibration ACOUSTICS-ENGINEERING, MECHANICAL
CiteScore
1.60
自引率
10.00%
发文量
0
审稿时长
12 months
期刊介绍: The International Journal of Acoustics and Vibration (IJAV) is the refereed open-access journal of the International Institute of Acoustics and Vibration (IIAV). The IIAV is a non-profit international scientific society founded in 1995. The primary objective of the Institute is to advance the science of acoustics and vibration by creating an international organization that is responsive to the needs of scientists and engineers concerned with acoustics and vibration problems all around the world. Manuscripts of articles, technical notes and letters-to-the-editor should be submitted to the Editor-in-Chief via the on-line submission system. Authors wishing to submit an article need to log in on the IJAV website first. Users logged into the website are able to submit new articles, track the status of their articles already submitted, upload revised articles, responses and/or rebuttals to reviewers, figures, biographies, photographs, copyright transfer agreements, and send comments to the editor. Each time the status of an article submitted changes, the author will also be notified automatically by email. IIAV members (in good standing for at least six months) can publish in IJAV free of charge and their papers will be displayed on-line immediately after they have been edited and laid-out. Non-IIAV members will be required to pay a mandatory Article Processing Charge (APC) of $200 USD if the manuscript is accepted for publication after review. The APC fee allows IIAV to make your research freely available to all readers using the Open Access model. In addition, Non-IIAV members who pay an extra voluntary publication fee (EVPF) of $500 USD will be granted expedited publication in the IJAV Journal and their papers can be displayed on the Internet after acceptance. If the $200 USD (APC) publication fee is not honored, papers will not be published. Authors who do not pay the voluntary fixed fee of $500 USD will have their papers published but there may be a considerable delay. The English text of the papers must be of high quality. If the text submitted is of low quality the manuscript will be more than likely rejected. For authors whose first language is not English, we recommend having their manuscripts reviewed and edited prior to submission by a native English speaker with scientific expertise. There are many commercial editing services which can provide this service at a cost to the authors.
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