Dynamics of a compressed Euler–Bernoulli beam on an elastic foundation with a partly prescribed discrete spectrum

IF 2.3 3区 工程技术 Q2 MECHANICS Acta Mechanica Pub Date : 2024-08-28 DOI:10.1007/s00707-024-04078-8
Andrei K. Abramian, Sergei A. Vakulenko, Wim T. van Horssen
{"title":"Dynamics of a compressed Euler–Bernoulli beam on an elastic foundation with a partly prescribed discrete spectrum","authors":"Andrei K. Abramian,&nbsp;Sergei A. Vakulenko,&nbsp;Wim T. van Horssen","doi":"10.1007/s00707-024-04078-8","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the dynamics of a compressed Euler-Bernoulli beam on a Winkler elastic foundation under the action of an external nonlinear force, which models a wind force, is studied. The beam is assumed to be long, and the lower part of its spectrum is prescribed. An asymptotic method is proposed to find the parameters of the beam, in order to have this prescribed lower part of the spectrum. All these parameters are necessary to guarantee the stability of the beam and to avoid resonances between the low frequency modes. These modes have special spatial supports that exclude a direct interaction between them. It is shown that the Galerkin system describing the time evolution can be decomposed into a system of almost independent equations which describes <i>n</i> independent nonlinear oscillators. Each oscillator has its own phase and frequency. It is shown that interaction between oscillators can exist only through high frequency modes.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"235 11","pages":"6679 - 6701"},"PeriodicalIF":2.3000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-024-04078-8","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0

Abstract

In this paper, the dynamics of a compressed Euler-Bernoulli beam on a Winkler elastic foundation under the action of an external nonlinear force, which models a wind force, is studied. The beam is assumed to be long, and the lower part of its spectrum is prescribed. An asymptotic method is proposed to find the parameters of the beam, in order to have this prescribed lower part of the spectrum. All these parameters are necessary to guarantee the stability of the beam and to avoid resonances between the low frequency modes. These modes have special spatial supports that exclude a direct interaction between them. It is shown that the Galerkin system describing the time evolution can be decomposed into a system of almost independent equations which describes n independent nonlinear oscillators. Each oscillator has its own phase and frequency. It is shown that interaction between oscillators can exist only through high frequency modes.

Abstract Image

Abstract Image

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
具有部分规定离散谱的弹性地基上的压缩欧拉-伯努利梁的动力学特性
本文研究了温克勒弹性地基上的受压欧拉-伯努利梁在模拟风力的非线性外力作用下的动力学特性。假定梁为长梁,并规定了其频谱的下半部分。提出了一种渐近方法来寻找梁的参数,以获得规定的下部频谱。所有这些参数对于保证梁的稳定性和避免低频模式之间的共振都是必要的。这些模态具有特殊的空间支撑,排除了它们之间的直接相互作用。研究表明,描述时间演化的 Galerkin 系统可以分解为一个几乎独立的方程系统,该系统描述 n 个独立的非线性振荡器。每个振荡器都有自己的相位和频率。研究表明,振荡器之间的相互作用只能通过高频模式存在。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Acta Mechanica
Acta Mechanica 物理-力学
CiteScore
4.30
自引率
14.80%
发文量
292
审稿时长
6.9 months
期刊介绍: Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
期刊最新文献
Size-dependent thermoelastic dissipation and frequency shift in micro/nano cylindrical shell based on surface effect and dual-phase lag heat conduction model Nonlinear free vibrations of sandwich plates with FG GPLR face sheets based on the full layerwise finite element method Investigation of static buckling and bending of nanoplates made of new functionally graded materials considering surface effects on an elastic foundation Estimation of dispersion and attenuation of Rayleigh waves in viscoelastic inhomogeneous layered half-space based on spectral method Airfoil-shaped vortex generators for separation control and drag reduction on wind turbine blades
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1