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2015 | Vol. 67, nr 4 | 311--330
Tytuł artykułu

On spatial behavior of the solution of a non-standard problem in linear thermoviscoelasticity with voids

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we study the constrained motion of a prismatic cylinder made of a thermoviscoelastic material with voids and subjected to final given data that are proportional, but not identical, to their initial values. We show how certain cross-sectional integrals of the solution spatially evolve with respect to axial variable. Some conditions are derived upon the proportionality coefficients in order to show that the integrals exhibit alternative behavior.
Wydawca

Rocznik
Strony
311--330
Opis fizyczny
Bibliogr. 19 poz., rys.
Twórcy
autor
  • Faculty of Mathematics “Alexandru Ioan Cuza" University of Iasi Blvd. Carol I. No. 11, 700506 Iasi, Romania, bucur.andreea.v@gmail.com
Bibliografia
  • 1. M.A. Goodman, S.C. Cowin, A continuum theory for granular materials, Arch. Ration. Mech. Anal., 44, 249–266, 1972.
  • 2. D. Iesan, On a theory of thermoviscoelastic materials with voids, J. Elasticity, 104, (1–2), 369–384, 2011.
  • 3. S.C. Cowin, J.W. Nunziato, Linear theory of elastic materials with voids, J. Elasticity, 13, 125–147, 1983.
  • 4. D. Iesan, A theory of thermoelastic materials with voids, Acta Mech., 60, 67–89, 1986.
  • 5. P.X. Pamplona, J.E. Munoz Rivera, R. Quintanilla, On uniqueness and analyticity in thermoviscoelastic solids with voids, J. Appl. Anal. and Comput., 1, 251–266, 2011.
  • 6. M.M. Svanadze, Potential method in the linear theory of viscoelastic materials with voids, J. Elasticity, 114, 101–126, 2014.
  • 7. S.K. Tomar, J. Bhagwan, H. Steeb, Time harmonic waves in a thermoviscoelastic material with voids, Journal of Vibration and Control, 20, 1119–1136, 2014.
  • 8. A. Bucur, Spatial behavior in linear theory of thermoviscoelasticity with voids, J. Thermal Stresses, 38, 2, 229–249, 2015, DOI:10.1080/01495739.2014.985566.
  • 9. K.A. Ames, L.E. Payne, P.W. Schaefer, On a nonstandard problem for heat conduction in a cylinder, Appl. Anal., 83, 125–133, 2004. 330 A. Bucur
  • 10. K.A. Ames, L.E. Payne, J.C. Song, On two classes of nonstandard parabolic problems, J. Math. Anal. Appl., 311, 254–267, 2005.
  • 11. S. Chiriµă, On some non-standard problems in linear thermoelasticity, J. Thermal Stresses, 32, 1256–1269, 2009.
  • 12. S. Chiriµă, M. Ciarletta, Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua, Eur. J. Mech. A/Solids, 18, 915–933, 1999.
  • 13. R. Quintanilla, B. Straughan, Energy bounds for some nonstandard problems in thermoelasticity, Proc. R. Soc. Lond. Ser. A, 461, 1147–1162, 2005.
  • 14. K.A. Ames, L.E. Payne, Asymptotic behavior for two regularizations of the Cauchy problem for the backward heat equation, Math. Models Methods Appl. Sci., 8, 187–202, 1998.
  • 15. K.A. Ames, G.W. Clark, J.F. Epperson, S.F. Oppenheimer, A comparison of regularizations for an illposed problem, Math. Comp., 67, 1451–1471, 1998.
  • 16. R.J. Knops, L.E. Payne, Alternative spatial growth and decay for constrained motion in an elastic cylinder, Math. Meth. Appl. Sci., 10, 281–310, 2005.
  • 17. S. Chiriµă, M. Ciarletta, Some non-standard problens related with the mathematical model of thermoelasticity with microtemperatures, J. Thermal Stresses, 36, 517–536, 2013.
  • 18. S. Chiriµă, M. Ciarletta, Spatial behavior for some non-standard problems in linear thermoelasticity without energy dissipation, J. Math. Anal. Appl., 367, (1), 58–68, 2010.
  • 19. E. Bulgariu, Alternative spatial growth and decay estimates for constrained motion in an elastic cylinder with voids, An. Stiinµ. Univ. "Al.I. Cuza" Iasi, Mat., 58, 341–359, 2011.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.baztech-28ae09f2-7656-4d12-8e36-0bfa4b0af099
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