Using Euler-Bernoulli beam theory an investigation is made of the dynamic behavior of an eccentric vertical circular shaft rotating in viscous medium. The shaft is subjected to linearly-varying tension and has distributed mass and elasticity. The mass eccentricity is assumed to be a deterministic function of the axial coordinate. The solution is obtained by modal analysis. An example is considered wherein the shaft is simply supported at the top and vertically guided at the bottom. Steady-state deflections and bending stresses are computed for a particular eccentricity function over a range of speeds of rotation which includes a resonant frequency.

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