Transient Resonance Oscillations of a System with Fractional Derivative Damping of Order ½

• Autorzy: Freundlich J. , Tylikowski A.
• Języki publikacji: EN

Abstrakty

EN

The solution of the equation of motion of a system with one degree of freedom and the fractional derivative damping of order 1/2 in the case of transition through resonance with a constant acceleration is presented in the paper. An integral expression of Duhamel type is used to obtain the system response. The method proposed by Miller and Ross [Miller and Ross, 1993] is used to find Green’s function. The solution can be used in analysis for more complex systems such rods or beams. Illustrative examples of transient responses for the considered system with the fractional and first order derivative damping model are presented.

Słowa kluczowe

EN

vibrations; fractional damping; transient resonance

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Research
• Rocznik: 2013
• Tom: Vol. 37, No. 4
• Strony: 27--33
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Freundlich J.

• Warsaw University of Technology, Poland

autor

Tylikowski A.

• Warsaw University of Technology, Poland

Bibliografia

• 1. Agrawal O. P., 2004, Analytical Solution for Stochastic Response of a Fractionally Damped Beam, ASME Journal of Vibration and Acoustics, 126, 561-566.
• 2. Bagley R. L., Torvik P. J., 1983a, Fractional Calculus - A Different Approach to the Analysis of Viscoelastically Damped structures, AIAA Journal, 21 (5), 741-748.
• 3. Bagley R. L., Torvik P. J., 1983b, A theoretical basis for the application of fractional Calculus to Viscoelasticity, Journal of Rheology, 27 (3), 201-210.
• 4. Caputo M., Mainardi F., 1971, A new Dissipation Model Based on Memory Mechanism, Pure and Applied Geophysics, 91 (8), 134-147.
• 5. Freundlich J., 2013, Vibrations of a Simply Supported Beam With a Fractional Derivative Order Viscoelastic Material Model - Supports Movement Excitation, Shock and Vibration, 20 (6), 1103-1112.
• 6. Kaliski S. (ed)., 1966, Drgania i fale, Państwowe Wydawnictwo Naukowe, Warszawa.
• 7. Miller K. S., Ross B., 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Willey & Sons Inc., New York.
• 8. Podlubny I., 1999, Fractional Differential Equations, Academic Press, San Diego.
• 9. Rossikhin Y. A., Shitikova M. V., 2010, Application of Fractional Calculus for dynamic Problems of Solid Mechanics: Novel Trends and Recent Results, Applied Mechanics Reviews, 63, 1-51.
• 10. Sakakibara S., 1997, Properties of Vibration with fractional derivative of order ½, JSME International Journal , Series C, 40, (3), 393-399.