二维运动物体弹性系统的能量和动量变化规律

IF 1.2 4区 物理与天体物理 Q4 ACOUSTICS
V. I. Erofeev, E. E. Lisenkova
{"title":"二维运动物体弹性系统的能量和动量变化规律","authors":"V. I. Erofeev,&nbsp;E. E. Lisenkova","doi":"10.1134/S1063771024601973","DOIUrl":null,"url":null,"abstract":"<p>The article considers a self-consistent problem on the dynamic behavior of a deformable system consisting of a two-dimensional elastic guide (subsystem 1) and a one-dimensional elastic object moving continuously along it (subsystem 2). Local and global energy and wave momentum change laws are presented for the case when the Lagrangians of the contacting subsystems depend on generalized coordinates and their derivatives lower than the second order with respect to all the spatiotemporal variables. The conditions of radiation in the considered class of systems are discussed. A comparative analysis of both dispersion and energy characteristics of bending waves propagating in plates is carried out for two different models. The critical velocities of a constant load moving along these plates are found. The dependence of critical velocities on the rigidity coefficient of an elastic base and the physicomechanical properties of a plate is established. The principal possibility of converting the energy of two-dimensional elastic guide oscillations into the energy of the translational motion of a one-dimensional object is demonstrated. The wave pressure force expressed in a universal form through the two-dimensional system Lagrangian acts as a mediator of such conversion. The dependence of the coefficient of wave energy conversion into the energy of the translational motion of an absolutely rigid fastening on its motion velocity and two-dimensional system parameters is constructed.</p>","PeriodicalId":455,"journal":{"name":"Acoustical Physics","volume":"71 3","pages":"301 - 311"},"PeriodicalIF":1.2000,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Energy and Momentum Change Laws for Two-Dimensional Elastic Systems with Moving Objects\",\"authors\":\"V. I. Erofeev,&nbsp;E. E. Lisenkova\",\"doi\":\"10.1134/S1063771024601973\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The article considers a self-consistent problem on the dynamic behavior of a deformable system consisting of a two-dimensional elastic guide (subsystem 1) and a one-dimensional elastic object moving continuously along it (subsystem 2). Local and global energy and wave momentum change laws are presented for the case when the Lagrangians of the contacting subsystems depend on generalized coordinates and their derivatives lower than the second order with respect to all the spatiotemporal variables. The conditions of radiation in the considered class of systems are discussed. A comparative analysis of both dispersion and energy characteristics of bending waves propagating in plates is carried out for two different models. The critical velocities of a constant load moving along these plates are found. The dependence of critical velocities on the rigidity coefficient of an elastic base and the physicomechanical properties of a plate is established. The principal possibility of converting the energy of two-dimensional elastic guide oscillations into the energy of the translational motion of a one-dimensional object is demonstrated. The wave pressure force expressed in a universal form through the two-dimensional system Lagrangian acts as a mediator of such conversion. The dependence of the coefficient of wave energy conversion into the energy of the translational motion of an absolutely rigid fastening on its motion velocity and two-dimensional system parameters is constructed.</p>\",\"PeriodicalId\":455,\"journal\":{\"name\":\"Acoustical Physics\",\"volume\":\"71 3\",\"pages\":\"301 - 311\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acoustical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1063771024601973\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acoustical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1063771024601973","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0

摘要

本文研究由二维弹性导轨(子系统1)和沿其连续运动的一维弹性物体(子系统2)组成的可变形系统的动力学行为自洽问题。给出了当接触子系统的拉格朗日量依赖于广义坐标及其对所有时空变量的二阶导数时的局部和全局能量和波动量变化规律。讨论了所考虑的这类系统的辐射条件。对比分析了两种不同模型下板内弯曲波的色散特性和能量特性。求出了沿这些板运动的恒定载荷的临界速度。建立了临界速度与弹性基刚度系数和板的物理力学性能的关系。证明了将二维弹性导轨振动能量转化为一维物体平移运动能量的主要可能性。通过二维拉格朗日系统以通用形式表示的波浪压力作为这种转换的中介。建立了绝对刚性固定体的波能转换为平动能的系数与运动速度和二维系统参数的关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Energy and Momentum Change Laws for Two-Dimensional Elastic Systems with Moving Objects

Energy and Momentum Change Laws for Two-Dimensional Elastic Systems with Moving Objects

Energy and Momentum Change Laws for Two-Dimensional Elastic Systems with Moving Objects

The article considers a self-consistent problem on the dynamic behavior of a deformable system consisting of a two-dimensional elastic guide (subsystem 1) and a one-dimensional elastic object moving continuously along it (subsystem 2). Local and global energy and wave momentum change laws are presented for the case when the Lagrangians of the contacting subsystems depend on generalized coordinates and their derivatives lower than the second order with respect to all the spatiotemporal variables. The conditions of radiation in the considered class of systems are discussed. A comparative analysis of both dispersion and energy characteristics of bending waves propagating in plates is carried out for two different models. The critical velocities of a constant load moving along these plates are found. The dependence of critical velocities on the rigidity coefficient of an elastic base and the physicomechanical properties of a plate is established. The principal possibility of converting the energy of two-dimensional elastic guide oscillations into the energy of the translational motion of a one-dimensional object is demonstrated. The wave pressure force expressed in a universal form through the two-dimensional system Lagrangian acts as a mediator of such conversion. The dependence of the coefficient of wave energy conversion into the energy of the translational motion of an absolutely rigid fastening on its motion velocity and two-dimensional system parameters is constructed.

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
Acoustical Physics
Acoustical Physics 物理-声学
CiteScore
1.60
自引率
50.00%
发文量
58
审稿时长
3.5 months
期刊介绍: Acoustical Physics is an international peer reviewed journal published with the participation of the Russian Academy of Sciences. It covers theoretical and experimental aspects of basic and applied acoustics: classical problems of linear acoustics and wave theory; nonlinear acoustics; physical acoustics; ocean acoustics and hydroacoustics; atmospheric and aeroacoustics; acoustics of structurally inhomogeneous solids; geological acoustics; acoustical ecology, noise and vibration; chamber acoustics, musical acoustics; acoustic signals processing, computer simulations; acoustics of living systems, biomedical acoustics; physical principles of engineering acoustics. The journal publishes critical reviews, original articles, short communications, and letters to the editor. It covers theoretical and experimental aspects of basic and applied acoustics. The journal welcomes manuscripts from all countries in the English or Russian language.
×
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:604180095
Book学术官方微信