長方形わく組の振動

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タイトル別名
  • Vibrations of Rectangular Frame Work
  • チョウホウケイワク クミ ノ シンドウ

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The vibrations in the plane and in the direction perpendicularly to the plane of rectangular frame work are discussed, of which both opposite bars are of same dimensions and of same materials, respectively. There is used such method that, from variation calculus to Lagrangian represented with displacements and unknown boundary values of each bar, the displacements are represented by unknown boundary values, and again, from the condition to make Lagrangian minimum, the unknown boundary values are determined and the frequency equations and the modes of vibrations are obtained. In the case of the vibrations of rectangular frame work, there are 24 boundary values in which 12 are represented by other 12 using the conditions of continuity at each vertex of rectangular frame work that the joints are rigid, for both vibrations in the plane and in the direction perpendicularly to the plane of rectangle, where in the former case the longitudinal and lateral vibrations and in the latter, the twisting and lateral ones are considered. There are three modes of vibrations in both cases, that is, symmetric and antisymmetric vibrations of all four bars, and symmetric vibration of a pair of bars and antisymmetric of other pair. It is, also, shown that the centre of gravity does not move in the vibrations which satisfy the frequency equations and modes obtained in this paper. Numerical calculations are carried out and the comparison are made among the results of calculations, experimental data and results by Rayleigh method.

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