The effect of tension on the dynamic behavior of eccentric shafts rotating in fluid medium

Using Euler-Bernoulli beam theory an investigation of the dynamic behavior of an eccentric rotating shaft, subject to linearly varying or constant tension, was made. The shaft has distributed mass and elasticity and is suspended in a fluid. Initial lack of straightness was also included in the analysis. The local mass eccentricity is assumed to be a deterministic function of the axial coordinate. For the variable-tension case the response was determined for a vertical shaft simply supported at the top and vertically guided at the bottom. The constant-tension case was analyzed for a shaft simply supported at its ends. The solution was obtained using modal analysis. It is in series form and is expressed in terms of characteristic functions of the free vibration shaft. External damping was linearized by equating the energy dissipated per revolution by quadratic and equivalent viscous damping. Displacements and stresses were computed along the shaft at a specific speed of rotation. Also maximum stress and displacement were computed for speeds in the neighborhood of a natural frequency. Results are given in graphical form for several values of the tension and different eccentricity functions.