非線形自由振動 : 非線形運動方程式の定常解問題-第 3 報

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タイトル別名
  • NONLINEAR FREE VIBRATION IN CONSERVATIVE FIELD : The Periodic Solution Problems of Nonlinear Equations of Motion-Part 3
  • 非線形運動方程式の定常解問題-3-非線形自由振動
  • ヒセンケイ ウンドウ ホウテイシキ ノ テイジョウカイ モンダイ 3 ヒセンケ

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抄録

This paper study periodic solutions of nonlinear autonomous equation of motion with one-degree-of-freedom in conservative field. Considering the relation between shapes of closed orbits on the phase plane and free vibration response shapes of the periodic solutions corresponding to the orbits, we derive the following conclusions. 1. The approximate periodic solution obtained by applying the cosine Fourier series to the equation of motion in conservative field uniformly converges to the exact periodic solution of it. 2. The approximate periodic solution obtained by applying the sine Fourier series does not generally converge to the exact solution. Then we seek the condition where the sine Fourier series can express the approximate solution which uniformly converges to the exact periodic solution.

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