Forced Oscillations of a Continuous Rotor with Geometric Nonlinearity. Subharmonic Resonances of Order 1/2 and Internal Resonance.

Abstract

Subharmonic resonances of order 1/2 of a continuous rotating shaft with distributed mass are discussed. The restoring force of the shaft exhibits geometric stiffening nonlinearity due to the extension of the shaft center line. It is assumed that a distributed lateral force, such as the gravity, acts on the rotor. The possibility of the occurrence of subharmonic resonances, the shapes of resonance curves, and internal resonance phenomena are investigated.