Analysis of bilinear oscillators under harmonic loading using nonlinear output frequency response functions

In this paper, the new concept of nonlinear output frequency response functions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the generalized frequency response functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs. Then, beginning with the demonstration that a bilinear oscillator can be approximated using a polynomial-type nonlinear oscillator, the NOFRFs are used to analyse the energy transfer phenomenon of bilinear oscillators in the frequency domain. The analysis provides insight into how new frequency generation can occur using bilinear oscillators and how the sub-resonances occur for the bilinear oscillators, and reveals that it is the resonant frequencies of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear oscillator model.