An analytical and meshless modeling for vibration analysis of an infinite quartz resonator with non-circular electrodes

Yang, Chen, Li, Peng, Wang, Bin, Liu, Dianzi, Qian, Zhenghua, Zaitsev, Boris, Kuznetsova, Iren and Hirose, Sohichi (2022) An analytical and meshless modeling for vibration analysis of an infinite quartz resonator with non-circular electrodes. Engineering Analysis with Boundary Elements, 144. pp. 33-43.

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Abstract

An analytical and meshless modeling for solving thickness shear vibration in an infinite piezoelectric quartz resonator with partial non-circular electrodes is proposed. Firstly, two-dimensional scalar differential equations derived by Tiersten and Smythe are adopted and transformed into the polar coordinate system. Secondly, displacement patterns for the electroded and unelectroded regions are assumed as a series of converging and outgoing cylindrical waves in the form of Bessel functions, where radiation conditions at infinity can be satisfied automatically. Finally, circumferential functions at interface are decomposed into Fourier series in order to deal with continuity conditions. It should be stressed that the general formulation proposed in this paper has a higher calculation accuracy and requires no division of the mesh compared to FEM/BEM, which can satisfy continuity conditions in an integrated manner over the whole interface or boundary. Resonance frequencies and mode shapes of different electrode shapes including circular, equilateral triangle, rectangular, elliptical, and pentagonal electrodes are numerically calculated and compared with FEM simulations, which efficiently validate high precision and wide applicability of this method. Utilizing this method, the influence of non-circular electrodes on the working performance of the quartz resonator is investigated systematically. The qualitative analysis and quantitative results obtained in this paper can provide the theoretical guidance for the design, measurement and manufacturing optimization of piezoelectric resonators.

Item Type:	Article
Additional Information:	Acknowledgments: This work was supported by the China Scholarships Council (No. 202106830041), the National Natural Science Foundation of China (12061131013, 11972276, 12172171 and 1211101401), the State Key Laboratory of Mechanics and Control of Mechanical Structures at NUAA (No. MCMS-E-0520K02), the Fundamental Research Funds for the Central Universities (NE2020002 and NS2019007), National Natural Science Foundation of China for Creative Research Groups (No. 51921003), the Start-up Fund supported by NUAA, National Natural Science Foundation of Jiangsu Province (BK20211176), Local Science and Technology Development Fund Projects Guided by the Central Government (2021Szvup061), Jiangsu High-Level Innovative and Entrepreneurial Talents Introduction Plan (Shuangchuang Doctor Program, JSSCBS20210166), and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). Prof. Iren Kuznetsova and Prof. Boris Zaitsev thank Russian Ministry of Science and Higher Education (FFWZ-2022-0002) for partial financial supports.
Faculty \ School:	Faculty of Science > School of Engineering
Depositing User:	LivePure Connector
Date Deposited:	26 Aug 2022 09:30
Last Modified:	16 Aug 2023 01:38
URI:	https://ueaeprints.uea.ac.uk/id/eprint/87635
DOI:	10.1016/j.enganabound.2022.08.002

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