%0 Journal Article
%T Dynamical analysis of linear single degree-of-freedom oscillator with fractional-order derivative<br>含分数阶微分的线性单自由度振子的动力学分析
%A Shen Yong-Jun
%A Yang Shao-Pu
%A Xing Hai-Jun
%A <br>申永军
%A 杨绍普
%A 邢海军
%J 物理学报
%D 2012
%I 
%X 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.
%K fractional-order derivative
%K averaging method
%K approximately analytical solution<br>分数阶微分
%K 平均法
%K 近似解析解
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=47EA7CFDDEBB28E0&jid=29DF2CB55EF687E7EFA80DFD4B978260&aid=78F360FC29C47911139655B0C5E412D2&yid=99E9153A83D4CB11&vid=1D0FA33DA02ABACD&iid=708DD6B15D2464E8&sid=676727212985921A&eid=676727212985921A&journal_id=1000-3290&journal_name=物理学报&referenced_num=0&reference_num=30