Dynamic characteristics of multi-disk shaft system using the vectors of solution coefficients

In this paper, a technique using relationships between the coefficient vectors of the differential equation solutions is extended to calculate the five lowest forward and backward whirling speeds of a multi-disk shaft system. To this end, the vertical and horizontal components of transverse vibrations are analysed using the Bernoulli-Eulerbeam model, including the gyroscopic effect of each disk. The aforementioned relationships obtained from the continuity equation and the equilibrium equations, when written in matrix form and compared to the conventional transfer matrices related to the state vector, present an advantage that reduces the number of multiplied matrices, when adjacent shaft segments have the same material properties and/or diameters. The associated whirling mode shapes are determined using the algebraic complements according to I.P. Natanson. The good agreement via a comparison between the obtained results and those available in the literature shows the efficiency and the accuracy of the presented method