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In this paper, an exact solution is presented for whirling analysis of rotors carrying concentrated masses. Effect of various parameters on the forward and backward frequencies are investigated including velocity of spin and quantity, translational inertia and position of the concentrated masses. It is shown that vibration characteristics of rotors can be affected by concentrated elements depended on the position of point masses and value of their translational inertia. The most advantage of the presented solution is that for rotors with any number of concentrated masses, all natural frequencies can be obtained through solution of a determinant of order 2.

Exact closed form solution for whirling analysis of Timoshenko rotors with multiple concentrated masses