On the Vibration of thin Cylindrical Shells under Internal Pressure
THOMPSON RAMO WOOLDRIDGE INC LOS ANGELES CA
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It is shown that for thin cylinders the internal pressure has a very significant effect on the natural vibration characteristics. For these cylinders, particularly those having smaller length-to-diameter ratios, the mode associated with the lowest frequency is in general not the simplest mode. In fact, the frequency spectrum may be so arranged that the frequency decreases with an increase in the number of circumferential nodes. The exact number of circumferential nodes which occur in the mode associated with the lowest frequency depends on the ratios ha, La, and the internal pressure, where h is the wall thickness, a is the cylinder radius, and L is the axial half-wave length. When the internal pressure is small, the number of circumferential nodes at the lowest frequency decreases rapidly with increasing internal pressure and the fundamental frequency - the lowest frequency at each internal pressure - increases rapidly with increasing internal pressure. At higher values of internal pressure the frequency spectrum tends to be arranged in the regular manner the frequency increases with the increasing number of circumferential nodes and the lowest frequency rises with the internal pressure, but at a slower rate.
- Theoretical Mathematics
- Structural Engineering and Building Technology