Contoured shaft and rotor dynamics

The dynamics of shaft–rotor systems, where the shaft profiles are contoured, are considered. Shafts with diameters which are functions of the shaft length are analysed. Procedures enabling the determination of the deflection, slope, bending moment and shear force at the extremities of the shaft are employed. Resonance, critical speed or whirling frequency conditions are computed using simple harmonic response methods. The response of the system for particular shaft–rotor dimensions and rotational speeds is determined, establishing the dynamic characteristics in the vicinity of the whirling speed. A cantilevered shaft–rotor system with an exponential – sinusoidal profile is investigated for purposes of illustration. The flexibility of the approach and the general applicability of the technique proposed is emphasised.