In this paper, the author established the fundamental equation of transverse vibrations of a rotating beam with variable rigidity under the influence of centrifugal force. Then he took the flexural rigidity EI and the cross-sectional area A of the beam as the functions of the distance x from its root, such as [function] and showed that in such special cases as
1) m = 5, n = 2
2) m = 6, n = 3
3) m = 6, n = 2
4) m = 7, n = 3
the equations are reduced to binomial equation and the solutions are obtained as the sum of hypergeometric series. Therefore the frequencies are determined by the eigen value method.
From these analysis, an interesting result was obtained ; if the frequencies of the vibration, which is perpendicular to the plane of rotation, are known, the frequencies of the vibration, which takes place in a plane making an arbitrary angle with the plane of rotation, can also be gained.
So, only the vibration perpendicular to the plane of rotation needes to be studied.
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