Abstract: The modal perturbation method is introduced to solve the modal characteristics of torsional vibration of a complicated nonhomogeneous shaft with variable cross-section. In this method, the analytical modal functions of the homogeneous shaft with uniform cross-section along its length, which has same end boundary conditions with the complicated shaft, are chosen as the basic functions for the approximate solution. By applying the Ritz expansion and the perturbation analysis, to solve the partial differential equation with variable coefficient is transferred into solving a set of the algebraic equations. Although the Ritz expansion that is often used in dynamic analysis of structures is applied in the suggested method, the eigenvalue problem of the Ritz generalized coordinates can be avoided. The modal characteristics of torsional vibration of the complicated shaft can be obtained by solving the algebraic equations one by one. It is shown by two numerical examples that the simplified method can be applied easily and has high precision.

Key words: Modal characteristics, Modal perturbation method, Nonhomogeneous shaft with variable cross-section, Torsional vibration