Superharmonic Resonance of Fractional-Order Mathieu-Duffing Oscillator

被引：10
作者：
Niu, Jiangchuan [1 ]
Li, Xiaofeng [2 ]
Xing, Haijun [3 ]
机构：
[1] Shijiazhuang Tiedao Univ, Sch Mech Engn, Shijiazhuang 050043, Hebei, Peoples R China
[2] Beijing Inst Technol, Sch Mechatron Engn, Beijing 100081, Peoples R China
[3] State Key Lab Mech Behav Traff Engn Struct & Syst, Shijiazhuang 050043, Hebei, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS | 2019年 / 14卷 / 07期
基金：
中国国家自然科学基金;
关键词：
VAN; STABILIZATION; BIFURCATION; SYSTEMS; MODEL;
D O I：
10.1115/1.4043523
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
The superharmonic resonance of fractional-order Mathieu-Duffing oscillator subjected to external harmonic excitation is investigated. Based on the Krylov-Bogolubov-Mitropolsky (KBM) asymptotic method, the approximate analytical solution for the third superharmonic resonance under parametric-forced joint resonance is obtained, where the unified expressions of the fractional-order term with fractional order from 0 to 2 are gained. The amplitude-frequency equation for steady-state solution and corresponding stability condition are also presented. The correctness of the approximate analytical results is verified by numerical results. The effects of the fractional-order term, excitation amplitudes, and nonlinear stiffness coefficient on the superharmonic resonance response of the system are analyzed in detail. The results show that the KBM method is effective to analyze dynamic response in a fractional-order Mathieu-Duffing system.
引用
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页数：10
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