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المستخلص
The main object of this thesis is the mathematical study of the vibration behavior in non-linear system described by coupled non-linear differential equations of the second order including quadratic and cubic non-linearties. The system consists of the main system and the absorber. The absorber is used to control (passive control) the main system vibrations. The two-degree-of-freedom system represents the vibration of dynamical system under either multi-external, multi-parametric or both external and parametric excitation forces have been considered. This system represents many applications in field of physics, mechanics, electronics and engineering.