Axial vibration of bars using fractional viscoelastic material models

• Autorzy: Łabędzki P. , Pawlikowski R. , Radowicz A.
• Języki publikacji: EN

Abstrakty

EN

This paper presents dynamic analysis of a bar with one end fixed and other free, loaded with force at its free end. The viscoelastic material of the bar is described by fractional models (Scot-Blair, Voigt, Maxwell and Zener models). Rayleigh-Ritz and Laplace transform methods were applied to obtain closed-form solution of the considered problem.

Słowa kluczowe

EN

fractional calculus; fractional viscoelastic material models; vibration of continuous system

PL

pochodna ułamkowa; modele materiałów lepkosprężystych; drgania układów ciągłych

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2018
• Tom: Vol. 29
• Strony: art. no. 2018009
• Opis fizyczny: Bibliogr. 9 poz., wykr.

Twórcy

autor

Łabędzki P.

• Kielce University of Technology, Faculty of Management and Computer Modelling, Al. Tysiąclecia Państwa Polskiego 7, 25-314 Kielce

autor

Pawlikowski R.

• Kielce University of Technology, Faculty of Mechatronics and Mechanical Engineering, Al. Tysiąclecia Państwa Polskiego 7, 25-314 Kielce

autor

Radowicz A.

• Kielce University of Technology, Faculty of Mechatronics and Mechanical Engineering, Al. Tysiąclecia Państwa Polskiego 7, 25-314 Kielce

Bibliografia

• 1. F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, World Scientific, 2010.
• 2. M. Di Paola, R. Heuer, A. Pirrotta, Fractional visco-elastic Euler-Bernoulli beam, International Journal of Solids and Structures, 50.22-23 (2013) 3505 - 3510.
• 3. R. Lewandowski, P. Wielentejczyk, Nonlinear vibration of viscoelastic beams described using fractional order derivatives, Journal of Sound and Vibration, 399 (2017) 228 - 243.
• 4. O. Martin, Nonlinear dynamic analysis of viscoelastic beams using a fractional rheological model, Applied Mathematical Modelling, 43 (2017) 351 - 359.
• 5. H. M. Srivastava, A. A. Kilbas, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, vol. 204, Elsevier, Amsterdam 2006.
• 6. R. Bagley, On the equivalence of the Riemann-Liouville and the Caputo fractional order derivatives in modelling of linear viscoelastic materials, Fractional Calculus and Applied Analysis, 10.2 (2007) 123 - 126.
• 7. N. Haymans, I. Podlubny, Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives, Rheologica Acta, 45.5 (2006) 765 - 771.
• 8. H. Cohen, F. Rodriguez Villegas, D. Zaiger, Convergence acceleration of alternating series, Experimental mathematics, 9.1 (2000) 3 - 12.
• 9. A. S. Novick, B. S. Berry Anelastic relaxation in crystalline solids, Academic Press, London, 1972.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).