Uncovering inner detached resonance curves in coupled oscillators with nonlinearity

Detached resonance curves have been predicted in multi-degree-of-freedom nonlinear oscillators, when subject to harmonic excitation. They appear as isolated loops of solutions in the main continuous frequency response curve and their detection may thus be hidden by numerical or experimental analysis. In this paper, an analytical approach is adopted to predict their appearance. Expressions for the amplitude-frequency equations and bifurcation curves are derived for a two degree-of-freedom system with cubic stiffness nonlinearity, and the effect of the system parameters is investigated. The interest is specifically towards the occurrence of closed detached curves appearing inside the main continuous frequency response curve, which may lead to a dramatic reduction of the amplitude of the system response. Both cases of hardening and softening stiffness characteristics are considered. The analytical findings are validated by numerical analysis.