El-Sayed, Ashraf TahaBauomy, Hany Samih2019-12-142019-12-142015Cited References in Web of Science Core Collection: 161077-5463https://doi.org/10.1177/1077546313514762https://cutt.ly/se6IUBvAccession Number: WOS:000360480500009In this paper, passive and active control methods are applied to reduce the torsional vibration of a nonlinear dynamical system. This system is subjected to multi parametric excitation forces and modeled by the coupled nonlinear differential equations. This leads to two degrees of freedom and three degrees of freedom when the torsional absorber is connected to the system. A multiple scale perturbation technique is applied to obtain an approximate solution and investigate the response of the system. The stability and the steady-state response of the system near the simultaneous sub-harmonic and internal resonances are studied and discussed using the frequency response function method. The numerical solution and chaotic response of the nonlinear dynamical system for different parameters are also studied. The simulation results are achieved using MATLAB 7.0 programs.enUniversity for Multiple scale methodnonlinear differential equationspassive and active controlstabilitytorsional vibrationArticlehttps://doi.org/10.1177/1077546313514762