Gyroscopic behaviour of stressed rotating shafts

An analysis is presented of the secondary effects due to deformation as a result of the shearing force, to the kinetic energy of rotation, and to the gyroscopic coupling, on the linearized equation of a straight shaft turning at a constant angular velocity and which is subjected to an axial torque and a compressive force. The local equations of motion of a section of shaft are derived and the magnitudes of the coupling terms are studied, non-dimensional variables being used. Results obtained by different authors in certain particular cases are rediscovered, and, in particular, the case of a shaft on short bearings is studied. Some comparisons of the theoretical results with those from experiments are given.