Stress and power as a response to harmonic excitation of a fractional anti‐Zener and Zener type viscoelastic body

Slađan Jelić, Dušan Zorica
{"title":"Stress and power as a response to harmonic excitation of a fractional anti‐Zener and Zener type viscoelastic body","authors":"Slađan Jelić, Dušan Zorica","doi":"10.1002/zamm.202300968","DOIUrl":null,"url":null,"abstract":"The stress as a response to strain prescribed as a harmonic excitation is examined in both transient and steady state regime for the viscoelastic body modeled by thermodynamically consistent fractional anti‐Zener and Zener models by the use of the Laplace transform method. Assuming strain as a sine function, the time evolution of power per unit volume, previously derived as a sum of time derivative of a conserved term, which represents the rate of change of stored energy, and a dissipative term, which represents dissipated power, is investigated when expressed through the relaxation modulus and creep compliance. Further, two forms of energy and two forms of dissipated power per unit volume are examined in order to see whether they coincide.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ZAMM - Journal of Applied Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/zamm.202300968","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

The stress as a response to strain prescribed as a harmonic excitation is examined in both transient and steady state regime for the viscoelastic body modeled by thermodynamically consistent fractional anti‐Zener and Zener models by the use of the Laplace transform method. Assuming strain as a sine function, the time evolution of power per unit volume, previously derived as a sum of time derivative of a conserved term, which represents the rate of change of stored energy, and a dissipative term, which represents dissipated power, is investigated when expressed through the relaxation modulus and creep compliance. Further, two forms of energy and two forms of dissipated power per unit volume are examined in order to see whether they coincide.
应力和功率对分数反齐纳和齐纳型粘弹性体谐波激励的响应
利用拉普拉斯变换方法,研究了热力学一致的分数反齐纳模型和齐纳模型所模拟的粘弹性体在瞬态和稳态状态下对谐波激励应变的应力响应。假定应变为正弦函数,研究了单位体积功率的时间演化过程,该过程以前是作为表示存储能量变化率的守恒项和表示耗散功率的耗散项的时间导数之和,通过松弛模量和蠕变顺应性来表示。此外,还研究了单位体积的两种能量形式和两种耗散功率形式,以确定它们是否一致。
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 求助全文
来源期刊
自引率
0.00%
发文量
0
×
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