Vibration of Two Rotor Systems:

Mechanical Vibration letting the model of a two rotor system illustrated in Figure (i). The mode of vibration is illustrated in Figure (ii). Let a is the distance of mode from left rotor.

              ∴        a + b = l

In the normal mode of vibration, the two rotors will vibrate in the opposite direction. At the node angle of the twist is equal to zero. Hence, even if the rotor is clamped, the similar vibration will continue to occur. Let the rotor be clamped at the node; there shall be two single rotor system, for which the neutral frequency is specified by the following formulae.

As these are the parts of the similar rotor, and so, both being part of the similar rotor they must have similar natural frequency

 Using Equations (66) and (64) values of a & b may be determined. Using value of a or b in Equation (62), natural frequency may be resolute. To plot mode shape, mark point of the node. Suppose some distance say 1 cm or 2 cm to begin from left end. Plot this with vertical line at left end. Alight this pt and node point and draw a line. This line shows the normal mode of vibration.