Note on the Effect of Rotation on the Frequencies of Lateral Vibrations of a Rod

Extract

In certain problems such as the vibration of airscrews or gyroplane rotor blades, account must be taken of the effect of the imposed rotation on the frequencies of vibration. A direct solution of the appropriate equation of motion is usually impracticable and in consequence recourse is had to the application of Rayleigh's Principle. But even this powerful device may involve increasing labour as ascending overtones are considered. In this note an empirical rule is indicated whereby the effect of rotation may be assessed. For a uniform rod the empirical rule is shown to be a very close approximation, particularly with ascending overtones. In other cases such as a tapered rod the rule is shown to apply, but the approximation is not so close.