Resonance Analysis of Fractional-Order Mathieu Oscillator-Reference-Cited by-同舟云学术

Resonance Analysis of Fractional-Order Mathieu Oscillator

Published:2018-03-23 Issue:5 Volume:13 Page:
ISSN:1555-1415
Container-title:Journal of Computational and Nonlinear Dynamics
language:en
Short-container-title:

Author:

Niu Jiangchuan¹,Gutierrez Hector²,Ren Bin¹

Affiliation:

1. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China e-mail:

2. Department of Mechanical & Aerospace Engineering, Florida Institute of Technology, Melbourne, FL 32901 e-mail:

Abstract

The resonant behavior of fractional-order Mathieu oscillator subjected to external harmonic excitation is investigated. Based on the harmonic balance (HB) method, the first-order approximate analytical solutions for primary resonance and parametric-forced joint resonance are obtained, and the higher-order approximate steady-state solution for parametric-forced joint resonance is also obtained, where the unified forms of the fractional-order term with fractional order between 0 and 2 are achieved. The correctness of the approximate analytical results is verified by numerical results. The effects of the fractional order and parametric excitation frequency on the resonance response of the system are analyzed in detail. The results show that the HB method is effective to analyze dynamic response in a fractional-order Mathieu system.

Funder

National Natural Science Foundation of China

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/doi/10.1115/1.4039580/6111964/cnd_013_05_051003.pdf

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