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.
Superharmonic Resonance of Fractional-Order Mathieu–Duffing Oscillator
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 10, 2018; final manuscript received April 9, 2019; published online May 13, 2019. Assoc. Editor: Brian Feeny.
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Niu, J., Li, X., and Xing, H. (May 13, 2019). "Superharmonic Resonance of Fractional-Order Mathieu–Duffing Oscillator." ASME. J. Comput. Nonlinear Dynam. July 2019; 14(7): 071005. https://doi.org/10.1115/1.4043523
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