Free Torsional Vibrations of a Single Rotor System

          Fig shows a shaft whose one end is fixed and the other end carries a rotor. This is known a single rotor system. When torsional vibrations are produced in this system, the natural frequency of torsional vibrations of this system is given by

Where                 C = Modulus of rigidity for shaft materials, 

                             J = Polar moment of inertia of shaft,

                             d = Diameter of shaft,

                             L = Length of shaft,

                             m = Mass of the rotor,

                             K = Radius of gyration of rotor, and 

                             I = Mass moment of inertia of rotor =   mK²

          The amplitude of vibration is maximum at free end where single rotor is attached where as the amplitude of vibrations is zero at fixed end of the shaft. This consideration will show that the amplitude of vibration is zero at A and maximum at B, as shown in Fig. It may be noted that the point or the section of the shaft whose amplitude of torsional vibration is zero is known as 'Node'. In other words, at the node, the shaft remains unaffected by the vibration.