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Abstract
This work is limited to multi-excitation forces which are external and/or parametric excitation forces. Multiple time scale perturbation technique is applied throughout to determine approximate solutions for the differential equations describing the system. Both frequency response equations and the phase-plane technique are applied to study the stability of the system. The phase-plane trajectories are good criterion for the presence of dynamic chaos. The effects of the different parameters are studied numerically. All reported resonance cases are studied numerically, applying Rung-Kutta fourth order method. By the end of the work we made a comparison with the available published work. Optimum working conditions of system are extracted when applying different cases of active controllers.