Critical Speeds of Rotating Shaft Subjected to Axial Loading and Tangential Torsion

Abstract

In this study the classical theory of the bending and twisting of thin rods is utilized and applied to the case of a rotating shaft subjected to axial loading and tangential torsion. The differential equation of small bending oscillations in its complex form is solved by using a three-term Galerkin approximation satisfying the boundary conditions term by term. Convergence of the solution is indicated by comparing the two-term and three-term approximations. The special cases of a stationary shaft subjected to axial load or twist are discussed briefly. Experimental results closely agree with the theoretically predicted values.