Dynamic response of a simply supported viscoelastic beam of a fractional derivative type to a moving force load

• Autorzy: Freundlich J.

Identyfikatory

DOI

10.15632/jtam-pl.54.4.1433

• Języki publikacji: EN

Abstrakty

EN

In the paper, the dynamic response of a simply supported viscoelastic beam of the fractional derivative type to a moving force load is studied. The Bernoulli-Euler beam with the fractional derivative viscoelastic Kelvin-Voigt material model is considered. The RiemannLiouville fractional derivative of the order 0 < α ¬ 1 is used. The forced-vibration solution of the beam is determined using the mode superposition method. A convolution integral of fractional Green’s function and forcing function is used to achieve the beam response. Green’s function is formulated by two terms. The first term describes damped vibrations around the drifting equilibrium position, while the second term describes the drift of the equilibrium position. The solution is obtained analytically whereas dynamic responses are calculated numerically. A comparison between the results obtained using the fractional and integer viscoelastic material models is performed. Next, the effects of the order of the fractional derivative and velocity of the moving force on the dynamic response of the beam are studied. In the analysed system, the effect of the term describing the drift of the equilibrium position on the beam deflection is negligible in comparison with the first term and therefore can be omitted. The calculated responses of the beam with the fractional material model are similar to those presented in works of other authors.

Słowa kluczowe

EN

fractional viscoelasticity; moving loads; beam vibrations; transient dynamic analysis

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2016
• Tom: Vol. 54 nr 4
• Strony: 1433--1445
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Freundlich J.

• Warsaw University of Technology, Faculty of Automotive and Construction Machinery Engineering, Warszawa, Poland

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniajacą naukę.