Analysis of non-linear dynamics of a two-degree-of-freedom vibration system with non-linear damping and non-linear spring

In this paper, the non-linear dynamics of a two-degree-of-freedom vibration system with non-linear damping and non-linear spring is studied. The analytic results show that the purposes of reducing amplitude and oscillation can be realized by adjusting properly the system parameters and considering the value of exciting frequency. The conclusions can provide some available evidences for the design and improvement of the non-linear absorber. Numerical simulations show the system exhibits periodic motions, quasiperiodic motions and chaotic motions.