Aeronautical and Space Sciences Japan

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The vibration of the framed structure has been analysed either by the exact method or by the lumped mass method. The former is too complicated to calculate the practical problems, and it wastes too much computing time. On the contrary the latter can be applied easily to the general practical problems, as it treats the problems as the eigenvalue problems of the statical stiffeness matrix. But its accuracy is not enough to calculate the natural vibration mode of the higher orders.
In this paper the author tried to establish the practical and accurate method. First he started from the basic differential equations of motions of the members of the framed structures in stead of the statical equation from which they started in the lumped mass method. Second he used the iteration method to solve the equation in stead of the exact method. As the result, the first approximate solution (the dynamic stiffeness matrix was expressed by the sum of the statical stiffeness matrix and the first order correction matrix for dynamic movement) proved to be enough to calculate the practical problem. Thus this method can be easily programmed by small amendment of the statical frame analysis program as in the cass of the lumped mass method.

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