In order to get the information on the dynamic strength of a vertical pipe for transporting mineral resources under the sea floor to a platform on the sea surface, the lateral vibration of the pipe due to external forces, such as waves, currents, impacts of icebergs, etc., must be analysed. As the first step for this purpose, the natural frequency of lateral vibration of the pipe has been analysed theoretically and experimentally, especially taking the effect of the flowing fluid in the pipe into consideration.
The results obtained are summarized as follows:
(1) The natural frequency of lateral vibration of the pipe decreases gradually as the velocity of inner fluid increases. There is the critical fluid velocity at which the natural frequency of the pipe becomes zero and its lateral vibration corresponding to the frequency vanishes. The value of the critical fluid velocity is smaller in cases of larger length and own weight of the pipe, larger compressive load applied axially at the top of the pipe, larger specific gravity of the inner fluid and smaller dimension of the cross-section of the pipe.
(2) The natural frequency of the pipe also decreases as the length and own weight of the pipe increase, and as the above-mentioned compressive load increases. Furthermore, the frequency becomes zero when the own weight and compressive load reach the buckling load of the pipe.
(3) In the practical range, the natural frequency of the pipe is little affected by the damping force due to the surrounding water.
(4) As the ratio of the mass of the surrounding water to that of the pipe with inner fluid increases, the natural frequency of the pipe decreases, but the ratio does not affect the critical fluid velocity.
(5) The same relationship between the natural frequency and the other quantities as mentioned above can be seen in cases of pipes with various kinds of supports. However, the frequency itself depends upon the condition for supporting the pipe at its ends. The frequency pertaining to the fixed-fixed supports of the pipe is almost twice as large as that pertaining to the pinned-pinned supports of the pipe. Besides, the frequency pertaining to the pipe which is fixed at the sea floor and pinned at the sea surface is about one and half times greater than that pertaining to the pinned-pinned supports of the pipe.
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