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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: Torsional vibration Modal characteristics
Nonhomogeneous shaft with variable cross-section Modal
perturbation method
CLC No: 032
Received 20040219, received in
revised form 20040810
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