EFFECT OF A SMALL TIP MASS ON THE VIBRATIONS OF A RAPIDLY ROTATING FLEXIBLE ROD

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Abstract
We consider a boundary-value problem associated with the vibrations of a rapidly rotating flexible rod with a small tip mass at its free end. The governing fourth-order differential equation involves two small parameters and has a turning point close to one of the endpoints. Hence, exponential-and logarithmic-type outer expansions alone are not adequate for the formation of a characteristic equation. Uniformly valid approximations are used to derive a consistent approximation to the eigenvalue relation. The expansion for the modification of the lowest eigenvalue due to the small tip mass is found to involve a different asymptotic sequence than the expan sions for modifications of the higher eigenvalues. Increasing the small tip mass decreases the lowest frequency of vibration, but increases the higher frequencies.

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