A Non-Linear Formulation of the Equations of Motion of a Rotating Bar.

摘要

The non-linear equations of motion of a slender beam rotating at constant angular velocity about a transverse axis are formulated. The state of stress in the bar is assumed to consist of two parts:the initial state of stress associated with the undisturbed equilibrium configuration of the rotating bar and the state of stress associated with the disturbed motion about the configuration of undisturbed equilibrium. The equations for the equilibrium state and the disturbed motion are separated and linearized,neglecting non-linear terms as well as gradients of initial displacements. As examples of the theory developed,the equations of motion for the longitudinal and flexural deformations of a rotating bar carrying a tip mass are derived. The longitudinal displacement and stress are shown to become unbounded at certain rotational velocities. (Author)