Transverse Vibrations and Stability of Systems with Gyroscopic Forces∗

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Abstract
Rotating shafts and pipes conveying fluid are examples of systems involving gyroscopic forces. The vibration and stability properties of such systems are often of practical interest to structural engineers. In this paper attention is focused on the characteristic curves of gyroscopic conservative systems in an appropriately chosen loading-frequency space. An upper bound to the fundamental frequency is obtained via the concept of a “corresponding nongyroscopic system.” The choice of the parameters and the resulting characteristic curves shed light on the stabilizing effect of gyroscopic forces. Special emphasis is placed on flutter instability. Three well-defined types of systems are discussed and several examples are analyzed. It is shown that various sequences of stable, divergence, and flutter regions may be exhibited as the loading parameter is increased, and that flutter instability may take place in an otherwise stable region.

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