Natural Transverse Oscillations of a Rotating Rod of Variable Cross Section

Abstract

The problem of natural oscillations of a rotating rod of variable cross section is considered. It is believed that the rod is rigidly attached at one end to a rotor with a constant speed orthogonal to the axis of rotation, the other end is assumed to be free. Flexural movements occur in the plane of rotation or perpendicular to it. To determine the natural oscillations, the Euler rod oscillation model is used, taking into account, in addition to the tensile force, the bond reaction force caused by the movements of the neutral axis. Using an original numerical-analytical method, the lower frequencies were calculated for the power and exponential laws of the cross section change.