Some insight into the appearance of detached resonance curves in the frequency response of nonlinear oscillators

Detached resonance curves, which lie inside or outside the main frequency response curve, have been theoretically predicted in multi degree-of-freedom nonlinear oscillators, when subject to harmonic excitation. The system parameters have been shown to critically affect their presence. This paper investigates the practical achievability of such features, when body geometry, weight and inertia effects are taken into account in a harmonically excited two degree-of-freedom mechanical system, consisting of coupled linear and nonlinear oscillators. Based on a simplified nominal model of the system, the Harmonic Balance Method is used to derive approximate analytical solutions for the frequency response curves, and numerical validation is performed. To investigate the effects in a practical system, a multi-body model of the mechanical system is assembled with feasible mass distribution and dimensions. These effects on the system response are then investigated. A time domain approach for identifying the physical parameters of the nonlinear model of the system, which is based on subspace methods, is also adopted, by applying a random excitation.