The response of a two-degree-of-freedom, controlled, autoparametric system to harmonic excitations is studied and solved. The objective of this research is to investigate the effect of linear absorber on the vibrating system and the saturation control of a linear absorber to reduce vibrations due to rotor blade flapping motion. The method of multiple scale perturbation technique is applied to obtain the periodic response equation near the primary resonance in the presence of internal resonance of the system. The stability of the obtained numerical solution is investigated using both phase plane methods and frequency response equations. Variation of some parameters leads to the bending of the frequency response curves and hence to the jump phenomenon occurrence. The reported results are compared to the available published work. © 2010 Elsevier Inc.
Sayed, M., & Kamel, M. (2011). Stability study and control of helicopter blade flapping vibrations. Applied Mathematical Modelling, 35(6), 2820–2837. https://doi.org/10.1016/j.apm.2010.12.002