{"title":"用弱形式正交元素法分析扇形薄板的横向自由振动","authors":"Hebin Liu, Hongzhi Zhong","doi":"10.1177/10775463231225276","DOIUrl":null,"url":null,"abstract":"The weak form quadrature element method is applied to free vibration analysis of thin sectorial plates with arbitrary vertex angles and boundary conditions. To tackle the strong stress singularity around the vertex, analytical displacement descriptions are introduced into the inner sectorial subdomain, while the outer annular subdomain is modeled by a single weak form quadrature thin plate element. The continuity on the interface between the two subdomains is enforced afterwards. Eventually, a generalized eigenvalue formulation is established after introducing Hamilton’s principle. The first six non-dimensional frequency parameters for various vertex angles and boundary conditions are obtained and compared with available results. Several typical free vibration modes are plotted. The accuracy, convergence rate, and computational cost of the present formulation are discussed at length.","PeriodicalId":508293,"journal":{"name":"Journal of Vibration and Control","volume":"65 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Transverse free vibration analysis of thin sectorial plates by the weak form quadrature element method\",\"authors\":\"Hebin Liu, Hongzhi Zhong\",\"doi\":\"10.1177/10775463231225276\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The weak form quadrature element method is applied to free vibration analysis of thin sectorial plates with arbitrary vertex angles and boundary conditions. To tackle the strong stress singularity around the vertex, analytical displacement descriptions are introduced into the inner sectorial subdomain, while the outer annular subdomain is modeled by a single weak form quadrature thin plate element. The continuity on the interface between the two subdomains is enforced afterwards. Eventually, a generalized eigenvalue formulation is established after introducing Hamilton’s principle. The first six non-dimensional frequency parameters for various vertex angles and boundary conditions are obtained and compared with available results. Several typical free vibration modes are plotted. The accuracy, convergence rate, and computational cost of the present formulation are discussed at length.\",\"PeriodicalId\":508293,\"journal\":{\"name\":\"Journal of Vibration and Control\",\"volume\":\"65 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Vibration and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1177/10775463231225276\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Vibration and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1177/10775463231225276","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Transverse free vibration analysis of thin sectorial plates by the weak form quadrature element method
The weak form quadrature element method is applied to free vibration analysis of thin sectorial plates with arbitrary vertex angles and boundary conditions. To tackle the strong stress singularity around the vertex, analytical displacement descriptions are introduced into the inner sectorial subdomain, while the outer annular subdomain is modeled by a single weak form quadrature thin plate element. The continuity on the interface between the two subdomains is enforced afterwards. Eventually, a generalized eigenvalue formulation is established after introducing Hamilton’s principle. The first six non-dimensional frequency parameters for various vertex angles and boundary conditions are obtained and compared with available results. Several typical free vibration modes are plotted. The accuracy, convergence rate, and computational cost of the present formulation are discussed at length.