Abstract
This paper reports an analytical study on the out-of-plane vibration and stability of a uniform beam attached to a rotating hub and carrying a rigid body at the other end. The parameters which govern the natural frequencies are the hub radius (root offset), speed of rotation of hub, the mass of the end body, its moment of inertia about an axis in the plane of rotation and through the centre of mass, the radial offset of the centre of mass from the beam end It is shown that for certain combinations of the system parameters a ‘tuned’ state (analogous to whirling of a shaft) is possible. It is also shown (hat for some combinations a natural frequency is zero (borderline of instability) even though the axial force distribution in the beam is tensile throughout. Negative centre of mass offset is a necessary but not sufficient condition for zero frequency to occur.
