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Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

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Abstract

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time (HB-AFT) domain technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

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Authors and Affiliations

  1. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, P. R. China

    Zhi-yong Zhang  (张智勇) & Yu-shu Chen  (陈予恕)

Authors
  1. Zhi-yong Zhang  (张智勇)
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  2. Yu-shu Chen  (陈予恕)
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Correspondence to Zhi-yong Zhang  (张智勇).

Additional information

Project supported by the National Natural Science Foundation of China (No. 10632040)

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Zhang, Zy., Chen, Ys. Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential. Appl. Math. Mech.-Engl. Ed. 35, 423–436 (2014). https://doi.org/10.1007/s10483-014-1802-9

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  • DOI: https://doi.org/10.1007/s10483-014-1802-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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