Open AccessDynamical analysis of linear single degree-of-freedom oscillator with fractional-order derivative
Author(s) -
Yongjun Shen,
Shaopu Yang,
Haijun Xing
Publication year - 2012
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.61.110505
Subject(s) - fractional calculus , mathematical analysis , amplitude , order (exchange) , derivative (finance) , resonance (particle physics) , mathematics , stiffness , physics , quantum mechanics , thermodynamics , finance , financial economics , economics
A linear single degree-of-freedom oscillator with fractional-order derivative is researched by the averaging method, and the approximately analytical solution is obtained. The effects of the parameters on the dynamical property, including the fractional coefficient and the fractional order, are characterized by the equivalent linear damping coefficient and the equivalent linear stiffness, and this conclusion is entirely different from the published results. The comparison of the analytical solution with the numerical results verifies the correctness of the approximately analytical results. The following analysis on the effects of the fractional parameters on the amplitude-frequency is fulfilled, and it is found that the fractional coefficient and the fractional order could affect not only the resonance amplitude through the equivalent linear damping coefficient, but also the resonance frequency by the equivalent linear stiffness.