Kotb, A. AEL-Sayed, A. TAmer, Y. A2019-12-032019-12-032016-090924-090Xhttps://doi.org/10.1007/s11071-016-2840-zhttps://link.springer.com/article/10.1007/s11071-016-2840-zAccession Number: WOS:000382399000026The aim of this paper was to study the nonlinear vibrations of a parametric excited Duffing oscillator with time delay feedback. At some values of the time delay can be used to suppress the vibration of the nonlinear system. The method of multiple scales perturbation is applied to obtain the analytical solution of the system and the frequency response equation near sub-harmonic resonance case. The stability of the obtained nonlinear solution is studied and solved numerically. The effects of the different parameters of the system behavior are investigated. Analytical solution in this paper is in good agreement with the numerical simulation.en-USUniversity for CHAOSABSORBERSUPPRESSIONSYSTEMStabilityTime delaySub-harmonic resonanceMultiple scales perturbationDuffing oscillatorArticlehttps://doi.org/10.1007/s11071-016-2840-z