Forced Oscillations of a Continuous Rotor with Nonlinear Spring Characteristcs. Vertical Shaft with Geometric Nonlinearity.

Abstract

Nonlinear forced oscillations of a vertical continuous rotating shaft with distributed mass are discussed. The restoring force of the shaft has geometric stiffening nonlinearity due to the extension of the shaft center line. The possibility of the occurrence of nonlinear forced oscillations at various subcritical speeds and the shapes of resonance curves at the major critical speeds and at some subcritical speeds are investigated. Consequently, the following is clarified : (a) the shape of resonance curves at the major critical speed becomes a hard-spring type, and (b) among various kinds of nonlinear forced oscillations, only some special kinds of summed-and-differential harmonic oscillations have possibility of occurrence.