期刊
ALEXANDRIA ENGINEERING JOURNAL
卷 57, 期 4, 页码 4009-4020出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.aej.2018.01.021
关键词
Homotopy perturbation method; Multiple-scales perturbation; Periodic delay Mathieu equation; Parametric resonance; Stability analysis
In the present work, the version of homotopy perturbation included time-scales is applied to the governing equation of time-periodic delay Mathieu equation. Periodical structure for the amplitude of the zero-order perturbation is constructed. The stability analysis is accompanied by considering three-time-scales. Approximate periodic solutions are derived to the second accuracy of perturbations at the harmonic resonance case as well as at the non-harmonic resonance case. Stability conditions are derived in both cases. Numerical calculations have been done to illustrate the stability behavior at both resonance and non-resonance case. It is shown that the time-delay has a destabilizing influence. We note that the delayed of the parametric excitation has a great interested and application to the design of nuclear accelerators. (C) 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V.
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