Resonances and resonant frequencies for a class of nonlinear systems

Resonant phenomena for a class of nonlinear systems, which can be described by a single-degree-of-freedom (sdof) model with a polynomial-type nonlinear stiffness, are investigated using nonlinear output frequency response functions (NOFRFs). The concepts of resonance and resonant frequencies are proposed for this class of nonlinear systems using the NOFRF concept, and the effects of damping on the resonances and resonant frequencies are analyzed. These results produce a novel interpretation of energy transfer phenomena in this class of nonlinear systems and show how the damping effect influences the system resonant frequencies and amplitudes. The results are important for the design and fault diagnosis of mechanical systems and structures which can be described by the sdof nonlinear model.