{"title":"用分数导数和弛豫时间修正的热弹性导热定律","authors":"A. Abouelregal","doi":"10.1142/s2251237320500033","DOIUrl":null,"url":null,"abstract":"(1) In the present work, a new modified thermoelasticity theory with fractional order has been constructed based on fractional calculus and Taylor series expansion of time-fractional order. The models of fractional thermoelasticity proposed by Sherief et al. [H. H. Sherief, A. M. A. El-Sayed and A. M. Abd El-Latief, Int. J. Solids Struct. 47, 269 (2010)], Ezzat [M. A. Ezzat, Phys. B 406, 30 (2011)] and Lord and Shulman with one relaxation time [H. W. Lord and Y. H. Shulman, J. Mech. Phys. Solids 15(5), 299 (1967)] as well as coupled thermoelasticity [M. A. Biot, J. Appl. Phys. 27, 240 (1956)] follow as limiting cases. This modified model is applied to an infinitely long annular cylinder. The inner and outer surfaces of the cylinder are traction free and subjected to known surrounding temperatures. Laplace transform technique will be used to get the solutions of all physical quantities. Some comparisons are shown in figures and tables to assess the effects of the fractional-order parameters in the studied fields. Results of some earlier researchers have been deduced from the current formulation. Finally, a conclusion about the new modified model has been promoted according to the analysis and numerical results.","PeriodicalId":16406,"journal":{"name":"Journal of Molecular and Engineering Materials","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/s2251237320500033","citationCount":"7","resultStr":"{\"title\":\"A Modified Law of Heat Conduction of Thermoelasticity with Fractional Derivative and Relaxation Time\",\"authors\":\"A. Abouelregal\",\"doi\":\"10.1142/s2251237320500033\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"(1) In the present work, a new modified thermoelasticity theory with fractional order has been constructed based on fractional calculus and Taylor series expansion of time-fractional order. The models of fractional thermoelasticity proposed by Sherief et al. [H. H. Sherief, A. M. A. El-Sayed and A. M. Abd El-Latief, Int. J. Solids Struct. 47, 269 (2010)], Ezzat [M. A. Ezzat, Phys. B 406, 30 (2011)] and Lord and Shulman with one relaxation time [H. W. Lord and Y. H. Shulman, J. Mech. Phys. Solids 15(5), 299 (1967)] as well as coupled thermoelasticity [M. A. Biot, J. Appl. Phys. 27, 240 (1956)] follow as limiting cases. This modified model is applied to an infinitely long annular cylinder. The inner and outer surfaces of the cylinder are traction free and subjected to known surrounding temperatures. Laplace transform technique will be used to get the solutions of all physical quantities. Some comparisons are shown in figures and tables to assess the effects of the fractional-order parameters in the studied fields. Results of some earlier researchers have been deduced from the current formulation. Finally, a conclusion about the new modified model has been promoted according to the analysis and numerical results.\",\"PeriodicalId\":16406,\"journal\":{\"name\":\"Journal of Molecular and Engineering Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2020-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1142/s2251237320500033\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Molecular and Engineering Materials\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s2251237320500033\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Molecular and Engineering Materials","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s2251237320500033","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 7
摘要
(1) 在分数阶微积分和时间分数阶的泰勒级数展开的基础上,构造了一个新的改进的分数阶热弹性理论。Sherief等人【H.H.Sherief,A.M.A.El Sayed和A.M.Abd El Latief,Int.J.Solids Struct.47269(2010)】、Ezzat【M.A.Ezzat,Phys.B 406,30(2011)】和Lord和Shulman提出的具有一个弛豫时间的分数热弹性模型【H.W.Lord和Y.H.Shulman,J.Mech.Phys.Solids 15(5),299(1967)】以及耦合热弹性【M.A.Biot,J。Appl。Phys。27240(1956)]作为限制性情况。该改进模型应用于无限长环形圆柱体。气缸的内表面和外表面无牵引力,并承受已知的周围温度。拉普拉斯变换技术将被用来得到所有物理量的解。图和表中显示了一些比较,以评估分数阶参数在所研究领域中的影响。一些早期研究人员的结果已经从目前的公式中推导出来。最后,根据分析和数值结果,对新的修正模型提出了结论。
A Modified Law of Heat Conduction of Thermoelasticity with Fractional Derivative and Relaxation Time
(1) In the present work, a new modified thermoelasticity theory with fractional order has been constructed based on fractional calculus and Taylor series expansion of time-fractional order. The models of fractional thermoelasticity proposed by Sherief et al. [H. H. Sherief, A. M. A. El-Sayed and A. M. Abd El-Latief, Int. J. Solids Struct. 47, 269 (2010)], Ezzat [M. A. Ezzat, Phys. B 406, 30 (2011)] and Lord and Shulman with one relaxation time [H. W. Lord and Y. H. Shulman, J. Mech. Phys. Solids 15(5), 299 (1967)] as well as coupled thermoelasticity [M. A. Biot, J. Appl. Phys. 27, 240 (1956)] follow as limiting cases. This modified model is applied to an infinitely long annular cylinder. The inner and outer surfaces of the cylinder are traction free and subjected to known surrounding temperatures. Laplace transform technique will be used to get the solutions of all physical quantities. Some comparisons are shown in figures and tables to assess the effects of the fractional-order parameters in the studied fields. Results of some earlier researchers have been deduced from the current formulation. Finally, a conclusion about the new modified model has been promoted according to the analysis and numerical results.