Some studies on rotors with polynomial type non-linear external and internal damping

Non-linear internal damping in rotating cylindrical shafts leads to isotropic non-linear circulatory and dissipative force fields. Orbital instability in such class of systems arises when the regenerative work due to circulatory forces exceeds the dissipative work done over an orbit. In this paper, stability condition for rotor shafts with polynomial type non-linear internal damping is derived and also it is shown that distortion of the critical orbit, which results in larger change in orbital path as compared to the change in enclosed area, may lead to stable orbit at normally unstable operating conditions. This principle is applied to stabilize a simple rotor with discontinuous stiffness characteristics, which come into effect on exceeding some threshold displacement of the rotor itself.