caa a22 4500 475839978 CHVBK 20180406123859.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1023/A:1004689114479 doi (NATIONALLICENCE)springer-10.1023/A:1004689114479 Analysis of nonlinear vibrations of a two-degree-of-freedom mechanical system with damping modelled by a fractional derivative [Elektronische Daten] [Yu.A. Rossikhin, M.V. Shitikova] Free damped vibrations of a mechanical two-degree-of-freedom system are considered under the conditions of one-to-one or two-to-one internal resonance, i.e., when natural frequencies of two modes - a mode of vertical vibrations and a mode of pendulum vibrations - are approximately equal to each other or when one natural frequency is nearly twice as large as another natural frequency. Damping features of the system are defined by the fractional derivatives with fractional parameters (the orders of the fractional derivatives) changing from zero to one. It is assumed that the amplitudes of vibrations are small but finite values, and the method of multiple scales is used as a method of solution. The model put forward allows one to obtain the damping coefficient dependent on the natural frequency of vibrations, so it has been shown that the amplitudes of vertical and pendulum vibrations attenuate by an exponential law with damping ratios which are exponential functions of the natural frequencies. Damped soliton-like solutions have been found analytically. Kluwer Academic Publishers, 2000 nonlinear vibrations nationallicence fractional derivative nationallicence 2dof mechanical system nationallicence energy exchange nationallicence Rossikhin Yu.A. Department of Theoretical Mechanics, Voronezh State Academy of Construction and Architecture, Ul. Kirova 3-75, 394018, Voronezh, Russia aut Shitikova M.V. Department of Theoretical Mechanics, Voronezh State Academy of Construction and Architecture, Ul. Kirova 3-75, 394018, Voronezh, Russia aut Journal of Engineering Mathematics Kluwer Academic Publishers 37/4(2000-05-01), 343-362 0022-0833 37:4<343 2000 37 10665 https://doi.org/10.1023/A:1004689114479 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004689114479 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rossikhin Yu.A. Department of Theoretical Mechanics, Voronezh State Academy of Construction and Architecture, Ul. Kirova 3-75, 394018, Voronezh, Russia aut NATIONALLICENCE 700 1- Shitikova M.V. Department of Theoretical Mechanics, Voronezh State Academy of Construction and Architecture, Ul. Kirova 3-75, 394018, Voronezh, Russia aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Kluwer Academic Publishers 37/4(2000-05-01), 343-362 0022-0833 37:4<343 2000 37 10665 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer