On the existence and uniqueness of the relaxation spectrum of viscoelastic materials. Part I. The main theorem

• Autorzy: Stankiewicz A.

Warianty tytułu

PL

O istnieniu i jednoznacznosci spektrum relaksacji materialow lepkosprezystych. Czesc I. Podstawowe twierdzenie

• Języki publikacji: EN

Abstrakty

EN

PL

Słowa kluczowe

EN

viscoelasticity; relaxation modulus; relaxation spectrum; completely monotone function; existence; polymer solution; Poisson's ratio; stress relaxation; Chebyshev function

• Wydawca: -
• Czasopismo: Teka Komisji Motoryzacji i Energetyki Rolnictwa
• Rocznik: 2010
• Tom: 10
• Opis fizyczny: p.379-387,fig.,ref.

Twórcy

autor

Stankiewicz A.

• Department of Technical Sciences, University of Life Sciences in Lublin, Lublin, Poland

Bibliografia

• Alzer H., Beig C. 2002.: Some classes of completely monotonie functions. Ann. Acad. Scient. Fennicae 27, 445-160.
• Ariderssen R. S., Loy R. J. 2002.: Rheologie al implications of completely monotone fading memory J. Rheol. 46(6), 1459- 1472.
• Aujla J. S. 2000.: Some Norm Inequalities for Completely Monotone Functions. SIMAX, 22(2), 569-573.
• Berg C., Pedersen H. L. 2001.: A completely monotone function related to the Gamma function. Journal of Computational and Applied Ivkthematics 133, 219-230.
• Bemste in S. N. 1928.: Sur les fonctions ábsolument monotones. Acta Mathematica, 1-66.
• Bochner S. 1955.: Harmonic Analys and the Theory of Probability University of California Press, Berkeley Los Angeles.
• Boltzmann L. 1876.: Zur Theorie der elastischen Nachwirkung. Ann. Phys. Chem. Erg. Bd. 7, 624-657.
• Brabec Ch. J., Rögl H., Schausberger A. 1997.: Investigation of relaxation properties of polymer melts by comparison of relaxation time spectra calculated with different algorithms. Rheol. Acta 36, 667-676.
• ChristensenR. M 1971.: Theory of Viscoelasticity. Academic Press, New York.
• Cocchini F., Nobile M. R. 2003.: Constrained inversion of rheological data to molecular weight distribution for polymer melts. Rheol. Acta 42, 232-242.
• Coleman B. D., Mizel V.J. 1967.: Norms and semi-groups in the theory of fading memory Archives for Rational Mechanics and Analysis 23, 87-123.
• Day A. 1972.: The Thermodynamics of Simple Materials with Fading Memory Springer Tracts in Natural Philosophy Volume 22, Springer-Verlag, New York.
• Derski W., Ziemba S. 1968.: Analiza modeli reologicznych. PWN Warszawa.
• Elster С., Honerkamp J., Weese J. 1991.: Using regularization methods for the determination of relaxation and retardation spectra of polymeric liquids. Rheol. Acta, 30,161-174.
• Fabrizio M., Morro A. 1992.: Mathematical Problems in Linear Viscoelasticity. SI AM Studies in Applied Mathematics 12, SIAM; Philadelphia.
• Galucio A. C., Deü J-F., Ohayon R. 2004.: Finite element formulation of viscoelastic sandwich beams using fractional derivative operators. Comp. Ivfechanics 33, 282-291.
• Gnnshpan A. Z., Ismail M. E. H., Milligan D. L. 2000.: On complete monotonocity and diesel fuel spray. Math. Intell. 22, 43-53.
• Gnperiberg G., LondenS. O., Staffans O. J. 1990.: Volterra Integral and Functional Equations. Cambridge Univ. Press, Cambridge.
• Hanyga A. 2005.: Viscous dissipation and completely monotonie relaxation moduli. Rheol. Acta 44, 614-621.
• L«maitre J. (Ed.) 2001.: Handbook of Materials Behavior Ivbdels, Academic Press, New York.
• Rao M A. 1999. Rheologyof Fluid and Semisolid Foods. Principles and Applications. Aspen Publishers, Inc., Gaithersbuig, Ivkryland.
• Richards D. St. P.: Positive definite symmetric functions on finite dimensional spaces . Statistics and Probab. Letters, 3, 325-329,1985.
• Stankiewicz A. 2004.: Ascheme for identification of relaxation spectrum of viscoelastic materials. Problemy Eksploatacji, 52(1), 121-133.
• Stankiewicz A. 2005.: Approximation of the retardation spectrum of viscoelastic plant materials using Legeridre functions. Acta Agrophysica, 6(3), 795-813.
• Stankiewicz A. 2009.: Identification of the relaxation spectrum by moment method approach:. Part I: Conceptual idea. Inżynieria Rolnicza, 6(115), 249-258. Part II: Theoretical properties and application. Inżynieria Rolnicza, 6(115), 259-26S.
• Widder D.V. 1946.: The Laplace Transform. Princeton Univ. Press, Princeton.
• ZiG., Bażant Z. P. 2002.: Continuous Relaxation Spectrum for Con:rete Creep andits Incorporation into Mcroplane Model M4. J. Eng. Mechanics, ASCE 128(12), 1331-1336.