Response of two-degree-of-freedom turbine-housing system with quadratic nonlinearity

A 2-degree-of-freedom model of a rotating machine with nonlinear springs of quadratic type is studied. The method of Multiple Scales is used to investigate the nonlinear oscillations of the forced system where the forcing is due to the eccentricity "e" of the rotor about its center of mass.

The behavior of the system for the primary resonances Q = LOI, Q = iV2, and internal resonance a;2 = 2a;i is analyzed. Other features, such as amplitude jump and saturation phenomenon, have been observed. The amplitudes versus detuning parameters for both cases are plotted. The critical values of mass ratios and spring ratios for the presence of an internal resonance are studied and interpreted for this particular application.