The analysis presented in this paper considers vibration of a beam of linearly varying cross-section that could represent a turbine blade of simple geometry The shear centre of each cross-section does not coincide with the centre of gravity, consequently the torsional and bending oscillations are ‘coupled’. The beam is attached to a hub of radius r, rotating at a constant angular velocity S, as shown in Fig. 1. The beam is allowed to vibrate in a plane making an angle (x/2-4) with the plane of rotation.