Abstract

A semi-analytic model is proposed to study the critical speeds and critical loads of the cantilever shaft-disk systems subjected to longitudinal loads. In the present work, both the exact and approximate stiffness influence coefficients of the longitudinally loaded cantilever shafts are derived. In order to obtain deeper insight into the dynamic behavior of such a shaft-disk system, the present shaft mathematical model has taken account of shear deformation effect. Because the exact stiffness influence coefficients of the shaft are transcendental and difficult to get their characteristics on longitudinal load intuitively, each stiffness influence coefficient is expanded in a Taylor’s series about the longitudinal load. Based on the present approximate stiffness influence coefficients, the critical speeds and critical loads of the cantilever shaft-disk systems can be easily and quickly obtained. Numerical simulations show that the present results are seen to be quite in agreement with the exact solutions.

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