title: Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation.
abstract: In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system.
authors: Transportation Institute, Shijiazhuang Tiedao University, Shijiazhuang 050043, China.
authors: Shao-Fang
authors: SF
authors: Wen
authors: Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China.
authors: Yong-Jun
authors: YJ
authors: Shen
authors: Hebei Vocational College of Rail Transportation, Shijiazhuang 052165, China.
authors: Xiao-Na
authors: XN
authors: Wang
authors: Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China.
authors: Shao-Pu
authors: SP
authors: Yang
authors: Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China.
authors: Hai-Jun
authors: HJ
authors: Xing