{"title":"用重心拉格朗日插值法分析了规则域和不规则域板的振动","authors":"Yen Liang Yeh","doi":"10.1177/1461348418819405","DOIUrl":null,"url":null,"abstract":"This paper uses the Barycentric Lagrange interpolation method to explore the free vibration of a plate with the regular and irregular domain using the Chebyshev function, allowing us to consider multiple dimensions. From our results, it can be shown that the Barycentric Lagrange interpolation method can solve three-dimensional problems. In the analysis, we can see that the Barycentric Lagrange interpolation method can solve the dynamic motion of the plate with regular domain, and the error of the simulation can be reduced to 0.15%. The effect of the geometric node number on the simulated error of the natural frequency of the plate is very profound. The Barycentric Lagrange interpolation method and the extrapolation difference method can solve the natural frequency of the plate with irregular domain. The error of the simulation on the natural frequency can be reduced to 1.084%. This allows us to understand the vibration of the plate with the regular and irregular domain under various boundary conditions quickly.","PeriodicalId":56118,"journal":{"name":"Journal of Low Frequency Noise Vibration and Active Control","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/1461348418819405","citationCount":"2","resultStr":"{\"title\":\"Vibration analysis of the plate with the regular and irregular domain by using the Barycentric Lagrange interpolation\",\"authors\":\"Yen Liang Yeh\",\"doi\":\"10.1177/1461348418819405\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper uses the Barycentric Lagrange interpolation method to explore the free vibration of a plate with the regular and irregular domain using the Chebyshev function, allowing us to consider multiple dimensions. From our results, it can be shown that the Barycentric Lagrange interpolation method can solve three-dimensional problems. In the analysis, we can see that the Barycentric Lagrange interpolation method can solve the dynamic motion of the plate with regular domain, and the error of the simulation can be reduced to 0.15%. The effect of the geometric node number on the simulated error of the natural frequency of the plate is very profound. The Barycentric Lagrange interpolation method and the extrapolation difference method can solve the natural frequency of the plate with irregular domain. The error of the simulation on the natural frequency can be reduced to 1.084%. This allows us to understand the vibration of the plate with the regular and irregular domain under various boundary conditions quickly.\",\"PeriodicalId\":56118,\"journal\":{\"name\":\"Journal of Low Frequency Noise Vibration and Active Control\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2018-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1177/1461348418819405\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Low Frequency Noise Vibration and Active Control\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1177/1461348418819405\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Earth and Planetary Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Low Frequency Noise Vibration and Active Control","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1177/1461348418819405","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Earth and Planetary Sciences","Score":null,"Total":0}
Vibration analysis of the plate with the regular and irregular domain by using the Barycentric Lagrange interpolation
This paper uses the Barycentric Lagrange interpolation method to explore the free vibration of a plate with the regular and irregular domain using the Chebyshev function, allowing us to consider multiple dimensions. From our results, it can be shown that the Barycentric Lagrange interpolation method can solve three-dimensional problems. In the analysis, we can see that the Barycentric Lagrange interpolation method can solve the dynamic motion of the plate with regular domain, and the error of the simulation can be reduced to 0.15%. The effect of the geometric node number on the simulated error of the natural frequency of the plate is very profound. The Barycentric Lagrange interpolation method and the extrapolation difference method can solve the natural frequency of the plate with irregular domain. The error of the simulation on the natural frequency can be reduced to 1.084%. This allows us to understand the vibration of the plate with the regular and irregular domain under various boundary conditions quickly.
期刊介绍:
Journal of Low Frequency Noise, Vibration & Active Control is a peer-reviewed, open access journal, bringing together material which otherwise would be scattered. The journal is the cornerstone of the creation of a unified corpus of knowledge on the subject.