Peng Z., Lang Z., Billings S., Lu Y.

There are considerable nonlinear systems existing in engineering practice, the investigation of nonlinear systems has provided better understanding of dynamical properties of cracked structures, mechanical vibration components with clearances, and mechanical devices with motion limiting stop, and so on. The importance of the resonance of linear systems in engineering practice has been well known, however no concepts equivalent to the resonance of linear systems are available. Nonlinear Output Frequency Response Functions (NOFRFs) are a new concept recently developed for the analysis of nonlinear systems in the frequency domain. Based on this concept, the output frequency behaviors of nonlinear systems can be expressed using a number of one-dimensional functions similar to the approach used in the traditional frequency response analysis of linear systems. In this paper, the definition of the concept of the resonance of the NOFRFs for SDOF nonlinear systems with polynomial type stiffness will be concerned, and the effect of the system damping on the resonances of the NOFRFs will be studied. The results provide a new insight into the energy transfer phenomenon caused by a system’s nonlinear effects. And the results presented in this paper are great helpful in design and control of mechanical systems which contain some components with polynomial stiffness properties and other engineering applications.