Stability of a rotating cantilever subjected to dissipative, aerodynamic, and transverse follower forces

Abstract

The problem of determining the state of stability of a slender cantilever rotating at a uniform speed and subjected to aerodynamic, dissipative, and transverse follower forces is investigated. The equations of motion for the flexural-torsional deformations of a slender rotating cantilever bar are derived from a conservation law that embodies the field equations for the disturbed state of stress in a solid rotating about a fixed axis relative to the initial state of stress associated with the undisturbed form of equilibrium of the rotating system. The associated non-self-adjoint boundary value problem is determined, and a suitable adjoint variational principle is derived. This variational principle serves as the basis for determining approximately the complex eigenvalues and hence the critical flutter values of the transverse follower force for prescribed values of the geometric and material properties of the system. Several graphs which illustrate the variation of the critical flutter load with the speed of rotation, hub radius, the internal damping parameters, aerodynamic load parameters, and the warping rigidity are presented.