Zastosowanie pochodnej ułamkowego rzędu do modelowania mieszanek mineralno-asfaltowych

• Autorzy: Grzesikiewicz W. , Zbiciak A.

Warianty tytułu

EN

Application of fractional order derivative to modelling of asphalt-aggregate mixtures

• Języki publikacji: PL

Abstrakty

EN

Asphalt-aggregate mixtures constitute basic component for the road pavements construction. The fundamental problem in the procedure of pavement design is to elaborate an appropriate constitutive model suited for the structural behaviour modelling within a wide range of mechanical and environmental loadings. The paper deals with the identification problem for a model representing constitutive properties of asphalt-aggregate mixtures. The constants characterising such a model should be evaluated based on expe-riments. There were analysed two viscoelastic rheological schemes. The classical Burgers model (Fig. 3a) contains linear elastic and viscous elements, while the Huet-Sayegh model (Fig. 3b) is composed of non-classical viscoelastic elements and its constitutive properties can be described using fractional derivatives. The results of cyclic tests of an asphalt-aggregate mixture were taken from the literature [8]. The experiments were carried out when assuming one-dimensional state of stress within the range of frequencies between 0.5 Hz and 35 Hz. The curve fitting procedure for both models was executed based on its complex moduli evaluation (Eqs. 11a and 11b). The obtained results show that by applying the fractional Huet-Sayegh model one can better fit the experiment in comparison with the classical Burgers model (see Figs. 4 and 5). Further investigations should be focused on description of non-linear effects using fractional and plastic elements. The plasticity phenomenon is important within the range of large intensities of loadings. The work on this area is currently underway by the authors.

Słowa kluczowe

PL

pochodne ułamkowe; mieszanki mineralno-asfaltowe; nawierzchnie asfaltowe

EN

fractional derivatives; asphalt-aggregate mixtures; asphalt pavements

• Wydawca: Wydawnictwo PAK
• Czasopismo: Pomiary Automatyka Kontrola
• Rocznik: 2011
• Tom: R. 57, nr 9
• Strony: 1048--1051
• Opis fizyczny: Bibliogr. 11 poz., rys., tab., wzor

Twórcy

autor

Grzesikiewicz W.

autor

Zbiciak A.

• Politechnika Warszawska, Instytut Pojazdów, ul. Narbutta 84, 02-524 Warszawa,

Bibliografia

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• [2] Kaczorek T.: Wybrane zagadnienia teorii układów niecałkowitego rzędu. Oficyna Wydawnicza Politechniki Białostockiej, Białystok 2009.
• [3] Katalog typowych konstrukcji nawierzchni podatnych i półsztywnych, IBDiM, GDDP, Warszawa 1997.
• [4] Kim Y. R.: Modeling of Asphalt Concrete. ASCE Press, McGraw-Hill, New York 2009.
• [5] MATLAB and Simulink online documentation, R2010a, March 2010 http://www.mathworks.com/access/helpdesk/help/helpdesk.html
• [6] Nowacki W. Teoria pełzania. Arkady, Warszawa 1963.
• [7] Piłat J., Radziszewski P.: Nawierzchnie asfaltowe. Wyd. Komunikacji i Łączności, Warszawa 2003.
• [8] Podlubny I.: Fractional Differential Equations. Mathematics in Science and Engineering, Vol. 198, Academic Press, 1999.
• [9] VEROAD User Manual, Ver. 2000. Netherlands Pavement Consultants bv.
• [10] Wang L.: Mechanics of Asphalt. Microstructure and Micromechanics. Mc Graw Hill, New York 2011.
• [11] Zbiciak A.: Dynamika materiałów i konstrukcji o nieklasycznych charakterystykach sprężysto-dyssypacyjnych. Prace Naukowe Politechniki Warszawskiej, Budownictwo z. 152, s. 1-156, OWPW, Warszawa 2010.