{"title":"利用标量微分方程和COMSOL对圆形石英谐振器进行有限元分析","authors":"Jun Shi, C. Fan, M. Zhao, Jia-shi Yang","doi":"10.1109/SPAWDA.2014.6998519","DOIUrl":null,"url":null,"abstract":"We study free vibrations of a circular AT-cut quartz resonator using the two-dimensional scalar differential equation by Tiersten and Smythe in conjunction with COMSOL. Resonant frequencies and mode shapes are obtained and compared with available experimental results as well as available analytical solutions of the scalar equation. The accuracy of various analytical solutions is examined.","PeriodicalId":412736,"journal":{"name":"Proceedings of the 2014 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Finite element analysis of circular quartz resonators using scalar differential equation and COMSOL\",\"authors\":\"Jun Shi, C. Fan, M. Zhao, Jia-shi Yang\",\"doi\":\"10.1109/SPAWDA.2014.6998519\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study free vibrations of a circular AT-cut quartz resonator using the two-dimensional scalar differential equation by Tiersten and Smythe in conjunction with COMSOL. Resonant frequencies and mode shapes are obtained and compared with available experimental results as well as available analytical solutions of the scalar equation. The accuracy of various analytical solutions is examined.\",\"PeriodicalId\":412736,\"journal\":{\"name\":\"Proceedings of the 2014 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-12-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2014 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SPAWDA.2014.6998519\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2014 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SPAWDA.2014.6998519","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Finite element analysis of circular quartz resonators using scalar differential equation and COMSOL
We study free vibrations of a circular AT-cut quartz resonator using the two-dimensional scalar differential equation by Tiersten and Smythe in conjunction with COMSOL. Resonant frequencies and mode shapes are obtained and compared with available experimental results as well as available analytical solutions of the scalar equation. The accuracy of various analytical solutions is examined.