THE FRACTIONAL DISTRIBUTED ORDER OSCILLATOR. A NUMERICAL SOLUTION
J. T. Katsikadelis
(UDC: 621.373.1:517.93)
Abstract:
The response of one-degree-of freedom systems with fractional distributed-order (FDO) damping is studied. The dynamics of such systems constitutes the problem of the fractional distributed-order oscillator. The investigation is achieved by developing an efficient numerical method for solving FDO differential equations. The problem is treated using two approaches. In the first approach, the system of the two coupled equations governing the response of the FDO oscillator is converted into a single FDO differential equation, while in the second approach the equations are treated as a system of FDO differential equations. Numerical examples are presented for free and forced vibrations of the FDO oscillator and useful conclusions are drawn. The resonance phenomenon is also elucidated.
