Skip to main content
Erschienen in: Meccanica 8/2017

08.11.2016

Generalized solutions of transient thermal shock problem with bounded boundaries

verfasst von: Y. Z. Wang, D. Liu, Q. Wang, J. Z. Zhou

Erschienen in: Meccanica | Ausgabe 8/2017

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this work, the generalized thermoelastic solutions with bounded boundaries for the transient shock problem are proposed by an asymptotic method. The governing equations are taken in the context of the generalized thermoelasticity with one relaxation time (L–S theory). The general solutions for any set of boundary conditions are obtained in the physical domain by the Laplace transform techniques. The corresponding asymptotic solutions for a thin plate with finite thickness, subjected to different sudden temperature rises in its two boundaries, are obtained by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, two specific problems with different boundary conditions have been conducted. The distributions of displacement, temperature and stresses, as well as the propagations, intersections and reflections of two elastic waves, named as thermoelastic wave and thermal wave separately, are obtained and plotted. These results are agreed with the results obtained in the existing literatures.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
2.
Zurück zum Zitat Lord HW, Shulman Y (1967) A generalized dynamic theory of thermoelasticity. J Mech Phys Solids 15:299–309ADSCrossRefMATH Lord HW, Shulman Y (1967) A generalized dynamic theory of thermoelasticity. J Mech Phys Solids 15:299–309ADSCrossRefMATH
6.
Zurück zum Zitat Abbas IA, Zenkour AM (2014) Two-temperature generalized thermoelastic interaction in an infinite fiber-reinforced anisotropic plate containing a circular cavity with two relaxation times. J Comput Theor Nanos 11:1–7CrossRef Abbas IA, Zenkour AM (2014) Two-temperature generalized thermoelastic interaction in an infinite fiber-reinforced anisotropic plate containing a circular cavity with two relaxation times. J Comput Theor Nanos 11:1–7CrossRef
7.
Zurück zum Zitat Youssef HM (2010) Theory of fractional order generalized thermoelasticity. J Heat Trans 132:061301–061307CrossRef Youssef HM (2010) Theory of fractional order generalized thermoelasticity. J Heat Trans 132:061301–061307CrossRef
8.
Zurück zum Zitat Sherief HH, El-Sayed AMA, Abd El-latief AM (2010) Fractional order theory of thermoelasticity. Int J Solids Struct 47:269–275CrossRefMATH Sherief HH, El-Sayed AMA, Abd El-latief AM (2010) Fractional order theory of thermoelasticity. Int J Solids Struct 47:269–275CrossRefMATH
9.
Zurück zum Zitat Povstenko YZ (2011) Fractional cattaneo-type equations and generalized thermoelasticity. J Therm Stresses 34:97–114CrossRef Povstenko YZ (2011) Fractional cattaneo-type equations and generalized thermoelasticity. J Therm Stresses 34:97–114CrossRef
11.
Zurück zum Zitat Tian XG, Shen YP (2012) Research progress in generalized thermoelastic problems. Adv Mech 42:1–11 Tian XG, Shen YP (2012) Research progress in generalized thermoelastic problems. Adv Mech 42:1–11
12.
Zurück zum Zitat El-Maghraby NM, Youssef HM (2004) State space approach to generalized thermoelastic problem with thermomechanical shock. Appl Math Comput 156:577–586MathSciNetMATH El-Maghraby NM, Youssef HM (2004) State space approach to generalized thermoelastic problem with thermomechanical shock. Appl Math Comput 156:577–586MathSciNetMATH
13.
Zurück zum Zitat Abbas IA (2014) Eigenvalue approach in a three-dimensional generalized thermoelastic interactions with temperatrue-dependent material properties. Comput Math Appl 68:2036–2056MathSciNetCrossRef Abbas IA (2014) Eigenvalue approach in a three-dimensional generalized thermoelastic interactions with temperatrue-dependent material properties. Comput Math Appl 68:2036–2056MathSciNetCrossRef
14.
Zurück zum Zitat Abbas IA (2015) Eigenvalue approach to fractional order generalized magneto-thermoelastic medium subjected to moving heat source. J Magn Magn Mater 377:452–459ADSCrossRef Abbas IA (2015) Eigenvalue approach to fractional order generalized magneto-thermoelastic medium subjected to moving heat source. J Magn Magn Mater 377:452–459ADSCrossRef
15.
Zurück zum Zitat El-Karamany AS, Ezzat MA (2004) Thermal shock problem in generalized thermoviscoelasticity under four theories. Int J Eng Sci 42:649–671MathSciNetCrossRefMATH El-Karamany AS, Ezzat MA (2004) Thermal shock problem in generalized thermoviscoelasticity under four theories. Int J Eng Sci 42:649–671MathSciNetCrossRefMATH
16.
Zurück zum Zitat Wang YZ, Zhang XB, Song XN (2012) A unified generalized thermoelasticity solution for the transient thermal shock problem. Acta Mech 223:735–743MathSciNetCrossRefMATH Wang YZ, Zhang XB, Song XN (2012) A unified generalized thermoelasticity solution for the transient thermal shock problem. Acta Mech 223:735–743MathSciNetCrossRefMATH
17.
Zurück zum Zitat Youssef HM (2006) Two-dimensional generalized thermoelasticity problem for a half-space subjected to ramp-type heating. Eur J Mech 25:745–763MathSciNetCrossRefMATH Youssef HM (2006) Two-dimensional generalized thermoelasticity problem for a half-space subjected to ramp-type heating. Eur J Mech 25:745–763MathSciNetCrossRefMATH
18.
Zurück zum Zitat Bagri A, Eslami MR (2007) A unified generalized thermoelasticity solution for cylinders and spheres. Int J Mech Sci 49:1325–1335CrossRef Bagri A, Eslami MR (2007) A unified generalized thermoelasticity solution for cylinders and spheres. Int J Mech Sci 49:1325–1335CrossRef
19.
Zurück zum Zitat Youssef HM (2006) Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading. Arch Appl Mech 75:553–565CrossRefMATH Youssef HM (2006) Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading. Arch Appl Mech 75:553–565CrossRefMATH
20.
Zurück zum Zitat Mukhopadhyay S, Kumar R (2008) A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity. Comput Math Appl 56:2329–2339MathSciNetCrossRefMATH Mukhopadhyay S, Kumar R (2008) A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity. Comput Math Appl 56:2329–2339MathSciNetCrossRefMATH
21.
Zurück zum Zitat Abbas IA, Zenkour AM (2015) The effect of magnetic field on thermal shock problem for a fiber-reinforced anisotropic half-space using Green-Naghdi’s theory. J Comput Theor Nano 12:438–442CrossRef Abbas IA, Zenkour AM (2015) The effect of magnetic field on thermal shock problem for a fiber-reinforced anisotropic half-space using Green-Naghdi’s theory. J Comput Theor Nano 12:438–442CrossRef
22.
Zurück zum Zitat Tian XG, Shen YP, Chen CQ, He TH (2006) A direct finite element method study of generalized thermoelastic problems. Int J Solids Struct 43:2050–2063CrossRefMATH Tian XG, Shen YP, Chen CQ, He TH (2006) A direct finite element method study of generalized thermoelastic problems. Int J Solids Struct 43:2050–2063CrossRefMATH
23.
Zurück zum Zitat Tehrani PH, Eslami MR (2000) Boundary element analysis of Green and Lindsay theory under thermal and mechanical shock in a finite domain. J Therm Stress 23:773–792CrossRef Tehrani PH, Eslami MR (2000) Boundary element analysis of Green and Lindsay theory under thermal and mechanical shock in a finite domain. J Therm Stress 23:773–792CrossRef
24.
Zurück zum Zitat Balla M (1991) Analytical study of the thermal shock problem of a half-space with various thermoelastic models. Acta Mech 89:73–92MathSciNetCrossRefMATH Balla M (1991) Analytical study of the thermal shock problem of a half-space with various thermoelastic models. Acta Mech 89:73–92MathSciNetCrossRefMATH
25.
Zurück zum Zitat Sherief HH, Elmisiery AEM, Elhagary MA (2004) Generalized thermoelastic problem for an infinite long hollow cylinder for short times. J Therm Stress 27:885–902CrossRef Sherief HH, Elmisiery AEM, Elhagary MA (2004) Generalized thermoelastic problem for an infinite long hollow cylinder for short times. J Therm Stress 27:885–902CrossRef
26.
Zurück zum Zitat Wang YZ, Zhang XB, Liu D (2013) Asymptotic analysis of generalized thermoelasticity for axisymmetric plane strain problem with temperature-dependent material properties. Int J Appl Mech 5:1350023–13500220CrossRef Wang YZ, Zhang XB, Liu D (2013) Asymptotic analysis of generalized thermoelasticity for axisymmetric plane strain problem with temperature-dependent material properties. Int J Appl Mech 5:1350023–13500220CrossRef
27.
Zurück zum Zitat Sherief HH, Youssef HM (2004) Short time solution for a problem in magneto-thermoelasticity with thermal relaxation. J Therm Stress 27:537–559CrossRef Sherief HH, Youssef HM (2004) Short time solution for a problem in magneto-thermoelasticity with thermal relaxation. J Therm Stress 27:537–559CrossRef
Metadaten
Titel
Generalized solutions of transient thermal shock problem with bounded boundaries
verfasst von
Y. Z. Wang
D. Liu
Q. Wang
J. Z. Zhou
Publikationsdatum
08.11.2016
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 8/2017
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-016-0527-7

Weitere Artikel der Ausgabe 8/2017

Meccanica 8/2017 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.