Saturation, stability and resonance of non-linear systems

Saturation phenomena may occur in non-linear vibrating systems. This phenomena is very useful in suppressing the undesired vibrations. In the present work saturation is investigated in a non-linear oscillating system subject to multi-parametric excitation. The system represents the vibration of a single-degree-of-freedom (SDOF) cantilever or the wing of an aircraft. Multiple scale perturbation method is applied to the system to obtain solution up to and including third-order approximations. The saturation phenomena is investigated at one of the extracted resonance cases. Other resonance cases are studied numerically. Effects of different parameters on saturation phenomena are studied. Stability of the system is investigated applying both frequency response function (FRF) and phase-plane trajectories. Some recommendations are given by the end of the work regarding best system behavior.