Higher Approximate Solutions of the Duffing Equation (Odd Order Superharmonic Resonances in the Hard Spring System)

Hideyuki Tamura, Takahiro Kondou, Atsuo Sueoka

研究成果: ジャーナルへの寄稿記事

抄録

In the previous paper, an algorithm was presented to obtain the periodic solutions and stability of nonlinear multi-degree-of-freedom systems with high speed and high accuracy, based on the harmonic balance method and the infinitesimal stability criterion. A revised algorithm is presented to give only odd order solutions which are composed of odd order harmonics only, and so reduces the dimensions of the amplitude vector and Jacobian matrix to about one-half of the previous one. The Duffing system with hard spring is analysed by this algorithm and the detailed frequency responses are computed for odd order superharmonic resonances (order 3, 5, 7, 9), which are the odd order solutions. The results are shown for each resonance region in terms of (a) maximum amplitudes and norms, (b) superharmonic amplitudes, (c) fundamental amplitudes, and (d) fundamental and superharmonic phase angles. Some of these are comfirmed by numerical simulation.

元の言語英語
ページ(範囲)1738-1747
ページ数10
ジャーナルNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
51
発行部数467
DOI
出版物ステータス出版済み - 1 1 1985
外部発表Yes

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Jacobian matrices
Degrees of freedom (mechanics)
Stability criteria
Frequency response
Computer simulation

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering

これを引用

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abstract = "In the previous paper, an algorithm was presented to obtain the periodic solutions and stability of nonlinear multi-degree-of-freedom systems with high speed and high accuracy, based on the harmonic balance method and the infinitesimal stability criterion. A revised algorithm is presented to give only odd order solutions which are composed of odd order harmonics only, and so reduces the dimensions of the amplitude vector and Jacobian matrix to about one-half of the previous one. The Duffing system with hard spring is analysed by this algorithm and the detailed frequency responses are computed for odd order superharmonic resonances (order 3, 5, 7, 9), which are the odd order solutions. The results are shown for each resonance region in terms of (a) maximum amplitudes and norms, (b) superharmonic amplitudes, (c) fundamental amplitudes, and (d) fundamental and superharmonic phase angles. Some of these are comfirmed by numerical simulation.",
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AU - Kondou, Takahiro

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