On Dynamic Stiffening of Flexible Bodies Having High Angular Velocity*

摘要

This paper presents an analysis of the dynamics of flexible bodies undergoing high angular velocity. It is shown that the high angular velocity produces a stiffening of the body, which can easily be neglected by an untimely, or inconsistent, linearization of the dynamical equations. The analysis presented is based on a linearization of second-order strain-displacement equations for elastic bodies. Kane's equations are then used to obtain the governing dynamical equations. It is asserted that this procedure produces a consistent linearization of the governing equations and, in the process, captures so-called #x201C;dynamic stiffening#x201D; terms that are sometimes lost with inconsistent linearizations. The analysis is illustrated by a series of examples of variously configured rotating beams and plates. In addition to deformations, the analysis is also used to compute restraint forces at the structural supports. It is seen that some of these forces can easily be missed with inconsistent linearization of the governing equations.