固定在长度有限的刚性支撑元件上的平面杆在自由端施加横向外力作用下的强制弯曲振动

IF 1.5 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Mechanics of Composite Materials Pub Date : 2024-07-02 DOI:10.1007/s11029-024-10206-1
V. N. Paimushin, V. M. Shishkin, S. F. Chumakova
{"title":"固定在长度有限的刚性支撑元件上的平面杆在自由端施加横向外力作用下的强制弯曲振动","authors":"V. N. Paimushin, V. M. Shishkin, S. F. Chumakova","doi":"10.1007/s11029-024-10206-1","DOIUrl":null,"url":null,"abstract":"<p>The problem of forced bending vibrations of a plane rod with a finite-length fastening section under the action of an external transverse force at its free end was solved. The classical Kirchhoff–Love model in the classical geometrically nonlinear approximation was used to describe the deformation process of the free part of the rod. The deformation of its fixed part was described by the Timoshenko refined shear model that takes into account transverse strains. The conditions of kinematic conjugation of the free and fixed parts of the rod were formulated. The equations of motion, the corresponding boundary conditions, and the force conditions of conjugation of the rod parts were obtained using the Hamilton–Ostrogradsky variational principle. An exact analytical solution of the problem of forced vibrations of a rod under the action of a harmonic transverse force at the free end of the unfastened part of the rod was deduced. Numerical experiments were carried out to study the resonant vibrations of rods made of unidirectional fiber composite. The effect of a noticeable increase of the amplitudes of transverse vibrations of the ends of the cantilever parts of the rods studied due to transverse contraction of the fixed section was revealed. Taking into account the transverse contraction caused an almost twofold reduction of the maximum transverse shear stresses in the fixed part of the duralumin rod.</p>","PeriodicalId":18308,"journal":{"name":"Mechanics of Composite Materials","volume":"30 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Forced Bending Vibrations of a Plane Rod Fixed on a Rigid Support Element of Finite Length Under the Action of an External Transverse Force Aplied to Its Free End\",\"authors\":\"V. N. Paimushin, V. M. Shishkin, S. F. Chumakova\",\"doi\":\"10.1007/s11029-024-10206-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The problem of forced bending vibrations of a plane rod with a finite-length fastening section under the action of an external transverse force at its free end was solved. The classical Kirchhoff–Love model in the classical geometrically nonlinear approximation was used to describe the deformation process of the free part of the rod. The deformation of its fixed part was described by the Timoshenko refined shear model that takes into account transverse strains. The conditions of kinematic conjugation of the free and fixed parts of the rod were formulated. The equations of motion, the corresponding boundary conditions, and the force conditions of conjugation of the rod parts were obtained using the Hamilton–Ostrogradsky variational principle. An exact analytical solution of the problem of forced vibrations of a rod under the action of a harmonic transverse force at the free end of the unfastened part of the rod was deduced. Numerical experiments were carried out to study the resonant vibrations of rods made of unidirectional fiber composite. The effect of a noticeable increase of the amplitudes of transverse vibrations of the ends of the cantilever parts of the rods studied due to transverse contraction of the fixed section was revealed. Taking into account the transverse contraction caused an almost twofold reduction of the maximum transverse shear stresses in the fixed part of the duralumin rod.</p>\",\"PeriodicalId\":18308,\"journal\":{\"name\":\"Mechanics of Composite Materials\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mechanics of Composite Materials\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://doi.org/10.1007/s11029-024-10206-1\",\"RegionNum\":4,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATERIALS SCIENCE, COMPOSITES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Composite Materials","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1007/s11029-024-10206-1","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATERIALS SCIENCE, COMPOSITES","Score":null,"Total":0}
引用次数: 0

摘要

研究解决了具有有限长度紧固截面的平面杆在自由端横向外力作用下的受迫弯曲振动问题。采用经典几何非线性近似的基尔霍夫-洛夫模型来描述杆自由部分的变形过程。其固定部分的变形由 Timoshenko 精炼剪切模型描述,该模型考虑了横向应变。制定了杆的自由部分和固定部分的运动共轭条件。利用汉密尔顿-奥斯特罗格拉茨基变分原理获得了运动方程、相应的边界条件以及杆件共轭的受力条件。推导出了杆的未紧固部分自由端在谐波横向力作用下的受迫振动问题的精确解析解。通过数值实验研究了单向纤维复合材料杆的共振振动。结果表明,由于固定部分的横向收缩,所研究杆件悬臂部分末端的横向振动幅度明显增大。考虑到横向收缩,硬铝杆固定部分的最大横向剪应力几乎降低了两倍。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

摘要图片

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
Forced Bending Vibrations of a Plane Rod Fixed on a Rigid Support Element of Finite Length Under the Action of an External Transverse Force Aplied to Its Free End

The problem of forced bending vibrations of a plane rod with a finite-length fastening section under the action of an external transverse force at its free end was solved. The classical Kirchhoff–Love model in the classical geometrically nonlinear approximation was used to describe the deformation process of the free part of the rod. The deformation of its fixed part was described by the Timoshenko refined shear model that takes into account transverse strains. The conditions of kinematic conjugation of the free and fixed parts of the rod were formulated. The equations of motion, the corresponding boundary conditions, and the force conditions of conjugation of the rod parts were obtained using the Hamilton–Ostrogradsky variational principle. An exact analytical solution of the problem of forced vibrations of a rod under the action of a harmonic transverse force at the free end of the unfastened part of the rod was deduced. Numerical experiments were carried out to study the resonant vibrations of rods made of unidirectional fiber composite. The effect of a noticeable increase of the amplitudes of transverse vibrations of the ends of the cantilever parts of the rods studied due to transverse contraction of the fixed section was revealed. Taking into account the transverse contraction caused an almost twofold reduction of the maximum transverse shear stresses in the fixed part of the duralumin rod.

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
Mechanics of Composite Materials
Mechanics of Composite Materials 工程技术-材料科学:复合
CiteScore
2.90
自引率
17.60%
发文量
73
审稿时长
12 months
期刊介绍: Mechanics of Composite Materials is a peer-reviewed international journal that encourages publication of original experimental and theoretical research on the mechanical properties of composite materials and their constituents including, but not limited to: damage, failure, fatigue, and long-term strength; methods of optimum design of materials and structures; prediction of long-term properties and aging problems; nondestructive testing; mechanical aspects of technology; mechanics of nanocomposites; mechanics of biocomposites; composites in aerospace and wind-power engineering; composites in civil engineering and infrastructure and other composites applications.
期刊最新文献
Analysis of Free Vibration and Low-Velocity Impact Response on Sandwich Cylindrical Shells Containing Fluid Mechanical Properties-Based Reliability Optimization Design of GFRP Culvert Dual-Phase Lag Model for a Solid Cylinder Made of Two Different Thermoelastic Materials Free Vibration Analysis of Functionally Graded Nano Graphene Composite Sandwich Plates Resting on a Winkler-Pasternak Foundation Multiphysics Homogenization and Localization of Wavy Brick-And-Mortar Architectures with Piezoelectric Effects
×
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