In this paper, a novel scheme for nonlinear displacement-dependent (NDD) damper is introduced. The damper is attached to a simple mass-spring-damper vibration system. The vibration system equipped with NDD damper is mathematically modeled and the nonlinear governing differential equation of the system is derived. To obtain the displacement of the system, the approximate analytical solution of the governing equation is elaborated using the multiple scales method. The advised approximate analytical algorithm is performed for several case studies and is also verified by the numerical forth-order Runge-Kutta method. In addition, the performance of the NDD damper is analyzed and compared with the performance of the traditional linear damper. It is found that the proposed NDD damper scheme along with the multiple scales method is not only feasible for vibration reduction but also yields satisfactory response performance rather than the existing traditional linear damper.

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