A refined multi-scale analysis of complex systems using frequency detuning: Perturbation around a nonlinear problem

The frequency detuning idea is further examined and fully extended to develop a refined multi-scale analysis procedure for more generic nonlinear systems of an inertially/damping/geometrical nonlinear type, aiming for a superior performance of predicting high-amplitude nonlinear responses, at the same time, without requiring a higher-order perturbation development. Briefly, frequency detuning means weakly nonlinear analysis/expansion is unfolded around a nonlinear oscillation problem, which is associated with a nonlinear (response) frequency rather than the commonly used linear frequency (i.e., perturbation around a nonlinear problem). Both frequency response curves (FRCs) and backbone curves (BBCs) are leveraged for a full comparison study regarding (frequency) detuned vs. traditional multi-scale methods (dMSM vs. MSM), with reference to numerical ones for verification. The results demonstrate superiority of dMSM in high-amplitude region when frequency detuning is employed.