{"title":"稳态受迫振动的修正传递矩阵法:一个杆单元系统","authors":"A. Lahe, Andres Braunbr¨uck, A. Klauson","doi":"10.3176/proc.2020.2.06","DOIUrl":null,"url":null,"abstract":". The Elements by a System of Transfer (EST) method offers exact solutions for various vibration problems of trusses, beams and frames. The method can be regarded as an improved or modified transfer matrix method where the roundoff errors generated by multiplying transfer arrays are avoided. It is assumed that in a steady state a bar/beam will vibrate with the circular frequency of a harmonic excitation force. The universal equation of elastic displacement (2nd/4th order differential equation) is described as a system of first order differential equations in matrix form. For the differential equations the compatibility conditions of a bar/beam element displacements at joint serve as essential boundary conditions. As the natural boundary conditions at joints, the equilibrium equations of elastic forces of bar/beam elements are considered. At the supports, restrictions to displacements (support conditions) have been applied. For steady-state forced vibration the phenomena of dynamic vibration absorption near the saddle points are observed and the response curves for displacement amplitude and elastic energy are calculated. The magnification factor at the excitation frequency is determined.","PeriodicalId":54577,"journal":{"name":"Proceedings of the Estonian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Modified transfer matrix method for steady-state forced vibration: a system of bar elements\",\"authors\":\"A. Lahe, Andres Braunbr¨uck, A. Klauson\",\"doi\":\"10.3176/proc.2020.2.06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". The Elements by a System of Transfer (EST) method offers exact solutions for various vibration problems of trusses, beams and frames. The method can be regarded as an improved or modified transfer matrix method where the roundoff errors generated by multiplying transfer arrays are avoided. It is assumed that in a steady state a bar/beam will vibrate with the circular frequency of a harmonic excitation force. The universal equation of elastic displacement (2nd/4th order differential equation) is described as a system of first order differential equations in matrix form. For the differential equations the compatibility conditions of a bar/beam element displacements at joint serve as essential boundary conditions. As the natural boundary conditions at joints, the equilibrium equations of elastic forces of bar/beam elements are considered. At the supports, restrictions to displacements (support conditions) have been applied. For steady-state forced vibration the phenomena of dynamic vibration absorption near the saddle points are observed and the response curves for displacement amplitude and elastic energy are calculated. The magnification factor at the excitation frequency is determined.\",\"PeriodicalId\":54577,\"journal\":{\"name\":\"Proceedings of the Estonian Academy of Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Estonian Academy of Sciences\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://doi.org/10.3176/proc.2020.2.06\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Estonian Academy of Sciences","FirstCategoryId":"103","ListUrlMain":"https://doi.org/10.3176/proc.2020.2.06","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Modified transfer matrix method for steady-state forced vibration: a system of bar elements
. The Elements by a System of Transfer (EST) method offers exact solutions for various vibration problems of trusses, beams and frames. The method can be regarded as an improved or modified transfer matrix method where the roundoff errors generated by multiplying transfer arrays are avoided. It is assumed that in a steady state a bar/beam will vibrate with the circular frequency of a harmonic excitation force. The universal equation of elastic displacement (2nd/4th order differential equation) is described as a system of first order differential equations in matrix form. For the differential equations the compatibility conditions of a bar/beam element displacements at joint serve as essential boundary conditions. As the natural boundary conditions at joints, the equilibrium equations of elastic forces of bar/beam elements are considered. At the supports, restrictions to displacements (support conditions) have been applied. For steady-state forced vibration the phenomena of dynamic vibration absorption near the saddle points are observed and the response curves for displacement amplitude and elastic energy are calculated. The magnification factor at the excitation frequency is determined.
期刊介绍:
The Proceedings of the Estonian Academy of Sciences is an international scientific open access journal published by the Estonian Academy of Sciences in collaboration with the University of Tartu, Tallinn University of Technology, Tallinn University, and the Estonian University of Life Sciences.
The journal publishes primary research and review papers in the English language. All articles are provided with short Estonian summaries.
All papers to be published in the journal are peer reviewed internationally.
The journal is open to word-wide scientific community for publications in all fields of science represented at the Estonian Academy of Sciences and having certain connection with our part of the world, North Europe and the Baltic area in particular.