{"title":"基于辛叠加法的Winkler弹性地基上矩形薄板和直角三角形板自由振动解析解","authors":"Hao-Jie Jiang, Tong-Bo Chen, Yu-Xiang Ren, Ning-Hua Gao","doi":"10.1093/jom/ufad032","DOIUrl":null,"url":null,"abstract":"Abstract Based on the symplectic superposition method, the free vibration models of rectangular and right-angle triangle plates on the Winkler elastic foundation are established in present paper, and the modes and frequencies are studied. In addition, the theoretical calculation model and finite element analysis model of rectangular thin plate and right-angle triangle plate on elastic foundation are established by using Mathematica software and ABAQUS software. It proves that the symplectic superposition method converges very fast and has a good consistency with the finite element simulation results. Analytical results show that foundation stiffness, aspect ratio and boundary condition have great influences on vibration frequency and mode shape for structures. This paper solved the free vibration problem of rectangular plate and right-angle triangle plate on elastic foundation by using symplectic superposition method. Compared with the inverse or semi-inverse method, this method avoids the process of assuming the form about the solution, hence the result of this method is completely rational.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":" 21","pages":"0"},"PeriodicalIF":1.5000,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytical solutions of free vibration for rectangular thin plate and right-angle triangle plate on the Winkler elastic foundation based on the symplectic superposition method\",\"authors\":\"Hao-Jie Jiang, Tong-Bo Chen, Yu-Xiang Ren, Ning-Hua Gao\",\"doi\":\"10.1093/jom/ufad032\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Based on the symplectic superposition method, the free vibration models of rectangular and right-angle triangle plates on the Winkler elastic foundation are established in present paper, and the modes and frequencies are studied. In addition, the theoretical calculation model and finite element analysis model of rectangular thin plate and right-angle triangle plate on elastic foundation are established by using Mathematica software and ABAQUS software. It proves that the symplectic superposition method converges very fast and has a good consistency with the finite element simulation results. Analytical results show that foundation stiffness, aspect ratio and boundary condition have great influences on vibration frequency and mode shape for structures. This paper solved the free vibration problem of rectangular plate and right-angle triangle plate on elastic foundation by using symplectic superposition method. Compared with the inverse or semi-inverse method, this method avoids the process of assuming the form about the solution, hence the result of this method is completely rational.\",\"PeriodicalId\":50136,\"journal\":{\"name\":\"Journal of Mechanics\",\"volume\":\" 21\",\"pages\":\"0\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2023-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/jom/ufad032\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/jom/ufad032","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MECHANICS","Score":null,"Total":0}
Analytical solutions of free vibration for rectangular thin plate and right-angle triangle plate on the Winkler elastic foundation based on the symplectic superposition method
Abstract Based on the symplectic superposition method, the free vibration models of rectangular and right-angle triangle plates on the Winkler elastic foundation are established in present paper, and the modes and frequencies are studied. In addition, the theoretical calculation model and finite element analysis model of rectangular thin plate and right-angle triangle plate on elastic foundation are established by using Mathematica software and ABAQUS software. It proves that the symplectic superposition method converges very fast and has a good consistency with the finite element simulation results. Analytical results show that foundation stiffness, aspect ratio and boundary condition have great influences on vibration frequency and mode shape for structures. This paper solved the free vibration problem of rectangular plate and right-angle triangle plate on elastic foundation by using symplectic superposition method. Compared with the inverse or semi-inverse method, this method avoids the process of assuming the form about the solution, hence the result of this method is completely rational.
期刊介绍:
The objective of the Journal of Mechanics is to provide an international forum to foster exchange of ideas among mechanics communities in different parts of world. The Journal of Mechanics publishes original research in all fields of theoretical and applied mechanics. The Journal especially welcomes papers that are related to recent technological advances. The contributions, which may be analytical, experimental or numerical, should be of significance to the progress of mechanics. Papers which are merely illustrations of established principles and procedures will generally not be accepted. Reports that are of technical interest are published as short articles. Review articles are published only by invitation.