Calculation of Natural Frequencies of Torsional Vibration of Shafts using Cauchy Sequence Iterative Methods

According to the true forms and the distribution of mass of the shafts, the dfferential-matrix equations of the torsional vibration with state variable x=[theta M](T) are set (theta, M express respectively the torsional angle and the torsional moment at the same cross-section). They are solved by means of Cauchy sequence iterative method. Then on the basis of the boundary conditions of the shafts, the natural frequencies of torsional vibration of the different shafts (the variable cross-section of uniform mass and non-uniform mass and the system of shafts) are calculated. Using the method in this paper, the amount of work of calculation is reduced greatly and the results of calculation are accurate compared with the approximate method in which a shaft of variable cross-section is replaced by many small segments of equal cross-section.