On the energy flux in elastic and inelastic bodies and cross-coupling flux between longitudinal and transversal elastic waves

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS
L.M.B.C. Campos, M.J.S. Silva
{"title":"On the energy flux in elastic and inelastic bodies and cross-coupling flux between longitudinal and transversal elastic waves","authors":"L.M.B.C. Campos,&nbsp;M.J.S. Silva","doi":"10.1016/j.wavemoti.2024.103446","DOIUrl":null,"url":null,"abstract":"<div><div>The energy balance equation, including not only the kinetic and deformation energy densities, but also the power of external forces, identifies the energy flux as minus the product of the velocity by the stress tensor: this result does not depend on constitutive relations and applies to elastic or inelastic matter. The simplest case is an isotropic pressure, when the energy flux equals its product by the velocity. In the linear case, the energy flux is obtained in elasticity for crystals and amorphous matter. An independent result is to show that, by inspection of any linear wave equation in a steady homogeneous medium, it is possible to ascertain whether the waves are (a) isotropic or not and (b) dispersive or not, with no need for an explicit solution. An application of this result to linear elastic waves shows that: (i) they are non-dispersive in crystals or amorphous matter; (ii) for the latter material, the longitudinal and transversal waves are isotropic, but their sum is not. A consequence of (ii) is that the superposition of longitudinal and transversal waves: (<span><math><mi>α</mi></math></span>) adds the two energy densities and powers of external forces; (<span><math><mi>β</mi></math></span>) adds, to the two energy fluxes, a third cross-coupling energy flux that is proportional to the dilatation of the longitudinal wave multiplied by the velocity of the transverse wave.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103446"},"PeriodicalIF":2.1000,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165212524001768","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0

Abstract

The energy balance equation, including not only the kinetic and deformation energy densities, but also the power of external forces, identifies the energy flux as minus the product of the velocity by the stress tensor: this result does not depend on constitutive relations and applies to elastic or inelastic matter. The simplest case is an isotropic pressure, when the energy flux equals its product by the velocity. In the linear case, the energy flux is obtained in elasticity for crystals and amorphous matter. An independent result is to show that, by inspection of any linear wave equation in a steady homogeneous medium, it is possible to ascertain whether the waves are (a) isotropic or not and (b) dispersive or not, with no need for an explicit solution. An application of this result to linear elastic waves shows that: (i) they are non-dispersive in crystals or amorphous matter; (ii) for the latter material, the longitudinal and transversal waves are isotropic, but their sum is not. A consequence of (ii) is that the superposition of longitudinal and transversal waves: (α) adds the two energy densities and powers of external forces; (β) adds, to the two energy fluxes, a third cross-coupling energy flux that is proportional to the dilatation of the longitudinal wave multiplied by the velocity of the transverse wave.
求助全文
约1分钟内获得全文 求助全文
来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
×
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