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言語
英語
著者
Ishibashi, Kazuki Department of Electronic Control Engineering, National institute of Technology, Hiroshima College,
内容記述(抄録等)
As is well known, Mathieu’s equation is a representative of mathematical models describing
parametric excitation phenomena. This paper deals with the oscillation problem for
Mathieu’s equation with two frequencies. The ratio of these two frequencies is not necessarily
a rational number. When the ratio is an irrational number, the coefficient of Mathieu’s
equation is is quasi-periodic, but not periodic. For this reason, the basic knowledge
for linear periodic systems such as Floquet theory is not useful. Whether all solutions of
Mathieu’s equation oscillate or not is determined by parameters and frequencies. Our results
provide parametric conditions to guarantee that all solutions are nonoscillatory. The
advantage of the obtained parametric conditions is that it can be easily checked. Parametric
nonoscillation region is drawn to understand these results easily. Finally, several
simulations are carried out to clarify the remaining problems.
主題
Nonoscillation
Parametric excitation
Mathieu’s equation
Frequencies
Quasi-periodic
掲載誌名
Applied Mathematics and Computation
346
開始ページ
491
終了ページ
499
ISSN
0096-3003
発行日
2019-04
DOI
出版者
Elsevier
資料タイプ
学術雑誌論文
ファイル形式
PDF
著者版/出版社版
著者版
部局
総合理工学部
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