円弧形棒の平面内の振動 : 固定-固定

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タイトル別名
  • Vibration of a Circular Arc Bar in its Plane : Both Ends Built-in
  • エンコケイボウ ノ ヘイメン ナイ ノ シンドウ コテイ-コテイ

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The Lagrangian in the vibration of a circular arc bar in its plane is discussed and the radial and tangential displacements are obtained in general forms. The frequency equations of a circular ring and a circular arc bar with hinged ends in the vibration in its plane are obtained and they are compared with the already known solutions. Then, the frequency equations of a circular arc bar with both ends built-in are obtained from the Lagrangian and the nondimensional frequencies are shown in figures. In the symmetric vibration of it, the effect of the slenderness ratio is large and the nondimensional frequencies are calculated in the cases where the slenderness ratio is very large and very small, 100 and 64 respectively. In the asymmetric one, its effect is small and those frequencies are calculated for both extreme cases. Also, for the vibration of a circular arc bar with both ends free, the nondimensional frequencies are calculated for both extreme cases.

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