{"title":"Conformable Fractional Order Theory in Thermoelasticity","authors":"Mohamed I. A. Othman, Haitham M. Atef","doi":"10.1134/S0025654423602252","DOIUrl":null,"url":null,"abstract":"<p>The fractional heat conduction equation in thermoelasticity by the definitions of Riemann-Liouville and Caputo has some shortcomings. In this paper, we introduce a conformable fractional order theory of thermoelasticity that remedies this shortcoming. Firstly, we derive the heat conduction equation based on the conformable fractional derivative. Then, the theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases. Finally, we apply these new governing equations to the problem of the general thermo material. The analytical expressions for physical quantities are obtained using normal mode analysis in the physical domain. These expressions are numerically calculated and graphically illustrated for a given material. The findings were predicted and tested in the presence and absence of fractional parameter.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 2","pages":"1180 - 1193"},"PeriodicalIF":0.6000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0025654423602252","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The fractional heat conduction equation in thermoelasticity by the definitions of Riemann-Liouville and Caputo has some shortcomings. In this paper, we introduce a conformable fractional order theory of thermoelasticity that remedies this shortcoming. Firstly, we derive the heat conduction equation based on the conformable fractional derivative. Then, the theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases. Finally, we apply these new governing equations to the problem of the general thermo material. The analytical expressions for physical quantities are obtained using normal mode analysis in the physical domain. These expressions are numerically calculated and graphically illustrated for a given material. The findings were predicted and tested in the presence and absence of fractional parameter.
期刊介绍：
Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.
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