具有弹性支承和连接边界条件的多跨弯曲梁面内自由振动分析

Q4 Energy
Haijun Zhou, Wanyou Li, Binglin Lü, Wenlong Li
{"title":"具有弹性支承和连接边界条件的多跨弯曲梁面内自由振动分析","authors":"Haijun Zhou, Wanyou Li, Binglin Lü, Wenlong Li","doi":"10.3969/J.ISSN.1006-7043.201107007","DOIUrl":null,"url":null,"abstract":"According to the vibration problem of a curved beam with elastic support boundary conditions,the in-plane free vibration characteristics of multi-span curved beams were analyzed using an improved Fourier series method.The transverse and tangential displacement functions were sought as a Fourier cosine series,and an auxiliary polynomial function was introduced to take all the relevant discontinuities of the elastic boundaries.The Rayleigh-Ritz method was used to solve Hamilton's equation,which is based on the energy principle,and a standard eigenvalue problem concerning the unknown displacement amplitudes was derived from which the natural frequencies and mode shapes can be solved.The results of single-span and two-span curved beams with free,simple supported,clamped,and elastic supported boundary conditions were obtained and compared with the results acquired from the finite element method(FEM) to validate the correctness of the presented method.Furthermore,the effect of the connecting stiffnesses between two-span curved beams on the first four frequencies was described.","PeriodicalId":35592,"journal":{"name":"哈尔滨工程大学学报","volume":"33 1","pages":"696-701"},"PeriodicalIF":0.0000,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"In-plane free vibration analysis of multi-span curved beams with elastic support and connecting boundary conditions\",\"authors\":\"Haijun Zhou, Wanyou Li, Binglin Lü, Wenlong Li\",\"doi\":\"10.3969/J.ISSN.1006-7043.201107007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"According to the vibration problem of a curved beam with elastic support boundary conditions,the in-plane free vibration characteristics of multi-span curved beams were analyzed using an improved Fourier series method.The transverse and tangential displacement functions were sought as a Fourier cosine series,and an auxiliary polynomial function was introduced to take all the relevant discontinuities of the elastic boundaries.The Rayleigh-Ritz method was used to solve Hamilton's equation,which is based on the energy principle,and a standard eigenvalue problem concerning the unknown displacement amplitudes was derived from which the natural frequencies and mode shapes can be solved.The results of single-span and two-span curved beams with free,simple supported,clamped,and elastic supported boundary conditions were obtained and compared with the results acquired from the finite element method(FEM) to validate the correctness of the presented method.Furthermore,the effect of the connecting stiffnesses between two-span curved beams on the first four frequencies was described.\",\"PeriodicalId\":35592,\"journal\":{\"name\":\"哈尔滨工程大学学报\",\"volume\":\"33 1\",\"pages\":\"696-701\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"哈尔滨工程大学学报\",\"FirstCategoryId\":\"1087\",\"ListUrlMain\":\"https://doi.org/10.3969/J.ISSN.1006-7043.201107007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Energy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"哈尔滨工程大学学报","FirstCategoryId":"1087","ListUrlMain":"https://doi.org/10.3969/J.ISSN.1006-7043.201107007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Energy","Score":null,"Total":0}
引用次数: 0

摘要

针对具有弹性支承边界条件的弯曲梁的振动问题,采用改进的傅立叶级数法分析了多跨弯曲梁的面内自由振动特性。将横向位移函数和切向位移函数求为傅里叶余弦级数,并引入辅助多项式函数取弹性边界的所有相关不连续点。采用基于能量原理的瑞利-里兹法求解Hamilton方程,导出了包含未知位移幅值的标准特征值问题,并由此求解了固有频率和模态振型。分别对自由、简支、固支和弹性支边界条件下的单跨和双跨弯曲梁进行了计算,并与有限元法计算结果进行了比较,验证了所提方法的正确性。进一步分析了两跨弯曲梁连接刚度对前4个频率的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
In-plane free vibration analysis of multi-span curved beams with elastic support and connecting boundary conditions
According to the vibration problem of a curved beam with elastic support boundary conditions,the in-plane free vibration characteristics of multi-span curved beams were analyzed using an improved Fourier series method.The transverse and tangential displacement functions were sought as a Fourier cosine series,and an auxiliary polynomial function was introduced to take all the relevant discontinuities of the elastic boundaries.The Rayleigh-Ritz method was used to solve Hamilton's equation,which is based on the energy principle,and a standard eigenvalue problem concerning the unknown displacement amplitudes was derived from which the natural frequencies and mode shapes can be solved.The results of single-span and two-span curved beams with free,simple supported,clamped,and elastic supported boundary conditions were obtained and compared with the results acquired from the finite element method(FEM) to validate the correctness of the presented method.Furthermore,the effect of the connecting stiffnesses between two-span curved beams on the first four frequencies was described.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
哈尔滨工程大学学报
哈尔滨工程大学学报 Energy-Nuclear Energy and Engineering
CiteScore
0.90
自引率
0.00%
发文量
6802
期刊介绍:
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信