Response of a rotating machine supported on nonlinear springs

The dynamic response of a two-degree-of-freedom rotating machine supported on hardening springs and viscous dampers is investigated. The rotating machine is subjected to internal forces caused by the eccentricity of the center of mass of the rotor. The equations of motion of the system were determined from Lagrange's equation. The system has cubic nonlinearities. The method of multiple scales was then used to determine the response of the system. The method predicts that primary resonance occurs when the excitation frequency Q is near the first modal frequecy o)i, and the second modal frequency 0)2. The method also predicts that the system can have internal resonance when o)2~3o)i. The response of the system was determined when the excitation frequency is near the first and the second modal frequency under noninternal resonance and internal resonance conditions.

The system exhibits the jump phenomena near the mode frequencies of the system. Unimodal response was also observed under internal resonance conditions when Ω≈~W2.