Abstarct: In this research, the application of nonlinear energy sink, including local and global sections on a linear oscillator to reduce vibrations has been investigated. This nonlinear absorber, which was numerically and analytically studied on various systems, is able to absorb and release energy from a primary system under external excitation in the form of one-way, passive and in a wide range of excitation frequencies. So far, in most researches devoted to nonlinear energy sink, nonlinear energy sink is considered only in global section, but in this research, the non-linear energy sink consists of two general and local parts. The global part is the section where the non-linear energy sink is in direct contact with the main system and the local section is only connected to mass of the nonlinear energy sink and has indirect interactions to energy transfer. Analytical modeling with slow invariant manifold method and numerical calculations of the proposed model is conducted by MATLAB software. The slow invariant manifold responses generated by the linear oscillator that is interacting with proposed nonlinear energy sink model have branches that reduce the vibrational absorption process of the system. By obtaining equilibrium and singular points, the system gives a periodic strongly modulated response, respectively. baxsed on these responses, several scenarios occur and in each case, the analytical and numerical results (modulated response) were compared and pumping energy in each scenario was investigated. The behavior of the system in the slowly invariant manifold analysis of the proposed system has three branches Instead of one, compared to a system without a local area. These branches are necessary for interpreting the system's behavior.